By your definition of continuity, none of your plotted functions are continuous. This is because in order for a limit limx→x0 f(x) lim x → x 0 f ( x) to exist, the function must be defined in some open interval containing x0 x 0. This won't happen in any of your functions at x0 = π x 0 = π. However, there are other definitions of ...Learn how to make a piecewise function continuous by finding values for two constantsLimit properties. (Opens a modal) Limits of combined functions. (Opens a modal) Limits of combined functions: piecewise functions. (Opens a modal) Theorem for limits of …Continuity of f: R → R at x0 ∈ R. Visualize x0 on the real number line. The definition of continuity would mean "if you approach x0 from any side, then it's corresponding value of f(x) must approach f(x0). Note that since x is a real number, you can approach it from two sides - left and right leading to the definition of left hand limits ...A function could be missing, say, a point at x = 0. But as long as it meets all of the other requirements (for example, as long as the graph is continuous between the undefined points), it’s still considered piecewise continuous. Piecewise Smooth. A piecewise continuous function is piecewise smooth if the derivative is piecewise continuous.If all preceding cond i yield False, then the val i corresponding to the first cond i that yields True is returned as the value of the piecewise function. If any of the preceding cond i do not literally yield False, the Piecewise function is returned in symbolic form. Only those val i explicitly included in the returned form are evaluated.Differentiability of Piecewise Defined Functions. Theorem 1: Suppose g is differentiable on an open interval containing x=c. If both and exist, then the two limits are equal, and the common value is g' (c). Proof: Let and . By the Mean Value Theorem, for every positive h sufficiently small, there exists satisfying such that: .In this section we will work a couple of examples involving limits, continuity and piecewise functions. Consider the following piecewise defined function Find so that is continuous at . To find such that is continuous at , we need to find such that In this case. On there other hand. Hence for our function to be continuous, we need Now, , and so ...In most cases, we should look for a discontinuity at the point where a piecewise defined function changes its formula. You will have to take one-sided limits separately since different formulas will apply depending on from which side you are approaching the point. Here is an example. Let us examine where f has a discontinuity. f(x)={(x^2 if x<1),(x if 1 le x < 2),(2x-1 if 2 le x):}, Notice ...lim x→af (x) = f (a) lim x → a. . f ( x) = f ( a) A function is said to be continuous on the interval [a,b] [ a, b] if it is continuous at each point in the interval. Note that this definition is also implicitly assuming that both f (a) f ( a) and lim x→af (x) lim x → a. . f ( x) exist. If either of these do not exist the function ...A piecewise function may have discontinuities at the boundary points of the function as well as within the functions that make it up. ... So we need to explore the three conditions of continuity at the boundary points of the piecewise function. How To. Given a piecewise function, determine whether it is continuous at the boundary points.Solving for x=1 we get 3 which confirms continuity for a=1. If 𝑎≠1 we would not be able to factor and would always get 0 in the numerator so a could only be 1. b can be anything because we would always get 3 for f(1) ... Turning a Piecewise Function into a Single Continuous Expression. 5.The piecewise continuous function is generally defined as a function that has a finite number of breaks in the function and doesn’t blow up to the infinity anywhere. It means this is a piecewise function but it does not go to the infinity. The piecewise continuous function is a function which is called piecewise continuous on a given …If you think about the graph of this function, it is a horizontal line on $(-\infty,-1]$, a line with some nonzero slope on $(-1,3)$, and then another horizontal line on $[3,\infty)$. What you are trying to do is find the equation of the line segment on $(-1,3)$ so it matches your two horizontal lines at the endpoints.In this section we will work a couple of examples involving limits, continuity and piecewise functions. Consider the following piecewise defined function Find so that is continuous at . To find such that is continuous at , we need to find such that In this case. On there other hand. Hence for our function to be continuous, we need Now, , and so ...Continuity of piecewise functions. Here we use limits to ensure piecewise functions are continuous. In this section we will work a couple of examples involving limits, continuity and piecewise functions. Consider the following piecewise defined function. f(x) = { x x−1 e−x + c if x < 0 and x ≠ 1, if x ≥ 0. f ( x) = { x x − 1 if x < 0 ...A piecewise continuous function is a function that is continuous except at a finite number of points in its domain. Note that the points of discontinuity of a piecewise continuous function do not have to be removable discontinuities. That is we do not require that the function can be made continuous by redefining it at those points. It …Then lim x → 0 − f(x) = lim x → 0 − (1 − x) = 1, lim x → 0 + f(x) = lim x → 0 + (x2) = 0, and f(0) = 02 = 0. DO : Check that the values above are correct, using the given piecewise definition of f. Since the limits from the left and right do not agree, the limit does not exist, and the function is discontinuous at x = 0. DO ...Piecewise functions are solved by graphing the various pieces of the function separately. This is done because a piecewise function acts differently at different sections of the nu...Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab...Limits of piecewise functions. In this video, we explore limits of piecewise functions using algebraic properties of limits and direct substitution. We learn that to find one-sided and two-sided limits, we need to consider the function definition for the specific interval we're approaching and substitute the value of x accordingly.The function that you showed is not continuous because it looks like two separate lines which don't ever connect. There are three main types of discontinuity: point, jump, and infinite. Point discontinuity, as said in the name, is when a function is not defined for a point. Jump discontinuity is the type of discontinuity your piecewise function ...It’s also in the name: piece. The function is defined by pieces of functions for each part of the domain. 2x, for x > 0. 1, for x = 0. -2x, for x < 0. As can be seen from the example shown above, f (x) is a piecewise function because it is defined uniquely for the three intervals: x > 0, x = 0, and x < 0.May 14, 2020 · Find the value of the constant c that makes the piecewise function continuous everywhere.Before working with this piecewise function f to make sure it's cont... Porsche has partnered with Mobileye to bring hands-free automated assistance and navigation functions to future sports cars. Porsche has partnered with Mobileye, the autonomous dri... 1. For what values of a a and b b is the function continuous at every x x? f(x) =⎧⎩⎨−1 ax + b 13 if x ≤ −1if − 1 < x < 3 if x ≥ 3 f ( x) = { − 1 if x ≤ − 1 a x + b if − 1 < x < 3 13 if x ≥ 3. The answers are: a = 7 2 a = 7 2 and b = −5 2 b = − 5 2. I have no idea how to do this problem. What comes to mind is: to ... 1. For what values of a a and b b is the function continuous at every x x? f(x) =⎧⎩⎨−1 ax + b 13 if x ≤ −1if − 1 < x < 3 if x ≥ 3 f ( x) = { − 1 if x ≤ − 1 a x + b if − 1 < x < 3 13 if x ≥ 3. The answers are: a = 7 2 a = 7 2 and b = −5 2 b = − 5 2. I have no idea how to do this problem. What comes to mind is: to ...Nov 16, 2021 · Find the domain and range of the function f whose graph is shown in Figure 1.2.8. Figure 2.3.8: Graph of a function from (-3, 1]. Solution. We can observe that the horizontal extent of the graph is –3 to 1, so the domain of f is ( − 3, 1]. The vertical extent of the graph is 0 to –4, so the range is [ − 4, 0). That might be ok if second part, when simplified, turned out to be a function of t2. The factor k/n does not depend on t, so we have. ln((1 +eδt)2/δ) − t. We have ln(ab) = b ln a, so we get: (2/δ) ln(1 +eδt) − t. The power series for ln(1 + x) and exp(x) are well-known, but a little effort is needed to get the series for ln(1 +et), and ...In this video I will show you How to Find a and b so that the Piecewise Function is Continuous Everywhere.Finding all values of a and b which make this piecewise function continuous. 2. Analysis of a Continuous Piecewise Function. 0. Simple Continuous Piecewise function. 1.By your definition of continuity, none of your plotted functions are continuous. This is because in order for a limit limx→x0 f(x) lim x → x 0 f ( x) to exist, the function must be defined in some open interval containing x0 x 0. This won't happen in any of your functions at x0 = π x 0 = π. However, there are other definitions of ...I need to determine whether this function is continuous at $(0,0)$ and support my answer. I know how to prove it isn't continuous, by finding a limit of the first function which isn't equal to $0$, but I'm not sure how to prove that it is continuous. 1. For what values of a a and b b is the function continuous at every x x? f(x) =⎧⎩⎨−1 ax + b 13 if x ≤ −1if − 1 < x < 3 if x ≥ 3 f ( x) = { − 1 if x ≤ − 1 a x + b if − 1 < x < 3 13 if x ≥ 3. The answers are: a = 7 2 a = 7 2 and b = −5 2 b = − 5 2. I have no idea how to do this problem. What comes to mind is: to ... 18. hr. min. sec. SmartScore. out of 100. IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)!Pulmonary function tests are a group of tests that measure breathing and how well the lungs are functioning. Pulmonary function tests are a group of tests that measure breathing an...The bathroom is one of the most used rooms in your house — and sometimes it can be the ugliest. So what are some things you can do to make your bathroom beautiful? “Today’s Homeown...If you are looking for the limit of a piecewise defined function at the point where the function changes its formula, then you will have to take one-sided limits separately since different formulas will apply depending on which side you are approaching from. Here is an example. For the following piecewise defined function f(x)={(x^2 if …continuity\:y=x^{3}-4,\:x=1 ; continuity\:y=\frac{x^{2}+x+1}{x} continuity\:\sqrt{4-x^{2}},x=2 ; continuity\:\left\{\frac{\sin(x)}{x}:x<0,1:x=0,\frac{\sin(x)}{x}:x>0\right\} …What questions may I be asked about continuity of piecewise functions? There are two main question types you will be asked about continuity of piecewise functions: 1.Stating values of x at which the function is not continuous. 2.Solving for a variable a that makes a piecewise function continuous. For these questions, it is important to remember ...Then lim x → 0 − f(x) = lim x → 0 − (1 − x) = 1, lim x → 0 + f(x) = lim x → 0 + (x2) = 0, and f(0) = 02 = 0. DO : Check that the values above are correct, using the given piecewise definition of f. Since the limits from the left and right do not agree, the limit does not exist, and the function is discontinuous at x = 0. DO ...So you have to check the continuity of each component function. Also a general and handy method is to check the continuity of the function using the sequential characterization of continuity in $\mathbb{R}^n,\forall n \geq 1$(and in metric spaces in general). See this.Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this siteContinuity of piece-wise functions. Here we use limits to ensure piecewise functions are continuous. In this section we will work a couple of examples involving limits, continuity and piecewise functions. Consider the following piecewise defined function. f(x) = { x x−1cos(−x) + C if x < 0, if x ≥ 0. Find C so that f is continuous at x = 0. In some cases, we may need to do this by first computing lim x → a − f(x) and lim x → a + f(x). If lim x → af(x) does not exist (that is, it is not a real number), then the function is not continuous at a and the problem is solved. If lim x → af(x) exists, then continue to step 3. Compare f(a) and lim x → af(x). This calculus video tutorial explains how to identify points of discontinuity or to prove a function is continuous / discontinuous at a point by using the 3 ...In general, finding a CDF requires solving inequalities. Recall the definition: the distribution function (CDF) of any random variable X is defined to be the function that sends real numbers x into the probability that X does not exceed x: FX(x) = Pr (X ≤ x). The event X ≤ x is a shorthand for the set of all observations ω ∈ Ω for which ...Muscle function loss is when a muscle does not work or move normally. The medical term for complete loss of muscle function is paralysis. Muscle function loss is when a muscle does...In this section we will work a couple of examples involving limits, continuity and piecewise functions. Consider the following piecewise defined function Find so that is continuous at . To find such that is continuous at , we need to find such that In this case. On there other hand. Hence for our function to be continuous, we need Now, , and so ...Finding all values of a and b which make this piecewise function continuous. 2. Analysis of a Continuous Piecewise Function. 0. Simple Continuous Piecewise function. 1.A Function Can be in Pieces. We can create functions that behave differently based on the input (x) value. A function made up of 3 pieces. Example: Imagine a function. when x is less than 2, it gives x2, when x is exactly 2 it gives 6. when x is more than 2 and less than or equal to 6 it gives the line 10−x. It looks like this: Piecewise-Defined Functions. A piecewise function is a function whose definition changes depending on the value of its argument. The function is defined by different formulas for different parts of its domain. For example, we can write the absolute value function \(f(x) = |x|\) as a piecewise function: Dec 4, 2012 ... Identify the discontinuity of the piecewise function graphically. ... There is a jump discontinuity at \begin{align*}x = 1\end{align*}. The ... The function f(x) = x2 is continuous at x = 0 by this definition. It is also continuous at every other point on the real line by this definition. If a function is continuous at every point in its domain, we call it a continuous function. The following functions are all continuous: 1 † In Mathematically, A function is said to be continuous at a point x = a, if. \ (\begin {array} {l}\lim_ {x\rightarrow a}\end {array} \) f (x) Exists, and. \ …1. In general when you want to find the derivative of a piece-wise function, you evaluate the two pieces separately, and where they come together, if the function is continuous and the derivative of the left hand side equals the derivative of the right hand side, then you can say that the function is differentiable at that point. i.e. if f(x) f ...The same applies to the tangent line. What if the function is not continuous at x=0 -- can you even have a tangent line? Is it possible for a line to touch only one point on a curve when that point is a discontinuity? This is encouraging you to go back and look at your basic understandings of a tangent line as well. You can check the continuity of a piecewise function by finding its value at the boundary (limit) point x = a. If the two pieces give the same output for this value of x, then the function is continuous. Let's explain this point through an example. Example 3. Check the continuity of the following piecewise functions without plotting the graph. how to: Given a piecewise function, determine whether it is continuous at the boundary points. For each boundary point \(a\) of the piecewise function, determine the left- and right-hand limits as \(x\) approaches \(a, \) as well as the function value at \(a\). Check each condition for each value to determine if all three conditions are satisfied.If you think about the graph of this function, it is a horizontal line on $(-\infty,-1]$, a line with some nonzero slope on $(-1,3)$, and then another horizontal line on $[3,\infty)$. What you are trying to do is find the equation of the line segment on $(-1,3)$ so it matches your two horizontal lines at the endpoints.Now with an executive team in place, Poppi co-founder Allison Ellsworth says the company is now “a well-oiled machine.” Consumer tastes are always shifting, but while traditional s...A piecewise function is a function that is defined in separate "pieces" or intervals. For each region or interval, the function may have a different equation or rule that describes it. We can evaluate piecewise functions (find the value of the function) by using their formulas or their graphs.The greatest integer (or floor) function and its graph, seen in calculus and computer science, exhibit similar features. We will take a peek into calculus and preview the related topics of one- and two-sided limits and continuity. Piecewise-defined functions appear frequently in these sections of a calculus course.Introduction. Piecewise functions can be split into as many pieces as necessary. Each piece behaves differently based on the input function for that interval. Pieces may be single points, lines, or curves. The piecewise function below has three pieces. The piece on the interval -4\leq x \leq -1 −4 ≤ x ≤ −1 represents the function f (x ...Identify the piece that describes the function at .In this case, falls within the interval, therefore use to evaluate.A function is said to be continous if two conditions are met. They are: the limit of the func... 👉 Learn how to find the value that makes a function continuos. Tour Start here for a quick overview of the site Help Center Detailed answers to any questions
👉 Learn how to find the value that makes a function continuos. A function is said to be continous if two conditions are met. They are: the limit of the func...Find the domain and range of the function f whose graph is shown in Figure 1.2.8. Figure 2.3.8: Graph of a function from (-3, 1]. Solution. We can observe that the horizontal extent of the graph is –3 to 1, so the domain of f is ( − 3, 1]. The vertical extent of the graph is 0 to –4, so the range is [ − 4, 0).Worked example: graphing piecewise functions. Google Classroom. About. Transcript. A piecewise function is a function that is defined in separate "pieces" or intervals. For each region or interval, the function may have a different equation or rule that describes it. We can graph a piecewise function by graphing each individual piece.In some cases, we may need to do this by first computing lim x → a − f(x) and lim x → a + f(x). If lim x → af(x) does not exist (that is, it is not a real number), then the function is not continuous at a and the problem is solved. If lim x → af(x) exists, then continue to step 3. Compare f(a) and lim x → af(x).Sep 6, 2017 · So you have to check the continuity of each component function. Also a general and handy method is to check the continuity of the function using the sequential characterization of continuity in $\mathbb{R}^n,\forall n \geq 1$(and in metric spaces in general). See this. Limits of piecewise functions: absolute value. Google Classroom. About. Transcript. This video focuses on finding the limit of |x-3|/ (x-3) at x=3 by rewriting it and examining it as a piecewise function. This approach helps us understand the behavior of the function for x values greater or less than 3, revealing that the limit doesn't exist.The bathroom is one of the most used rooms in your house — and sometimes it can be the ugliest. So what are some things you can do to make your bathroom beautiful? “Today’s Homeown...Example 1.1 Find the derivative f0(x) at every x 2 R for the piecewise defined function f(x)= ⇢ 52x when x<0, x2 2x+5 when x 0. Solution: We separate into 3 cases: x<0, x>0 and x = 0. For the first two cases, the function f(x) is defined by a single formula, so we could just apply di↵erentiation rules to di↵erentiate the function.This can be applied here, by considering, at each "transition" between one piece of the function to the next, whether the functions composing the part to the right and left of the boundary agree at the boundary.Limits of piecewise functions. In this video, we explore limits of piecewise functions using algebraic properties of limits and direct substitution. We learn that to find one-sided and two-sided limits, we need to consider the function definition for the specific interval we're approaching and substitute the value of x accordingly.Continuity and Discontinuity of Functions. Functions that can be drawn without lifting up your pencil are called continuous functions. You will define continuous in a more mathematically rigorous way after you study limits. There are three types of discontinuities: Removable, Jump and Infinite.Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab... The function f(x) = x2 is continuous at x = 0 by this definition. It is also continuous at every other point on the real line by this definition. If a function is continuous at every point in its domain, we call it a continuous function. The following functions are all continuous: 1 † Finding all values of a and b which make this piecewise function continuous. 2. Analysis of a Continuous Piecewise Function. 0. Simple Continuous Piecewise function. 1.Hence the function is continuous at x = 1. (iii) Let us check whether the piece wise function is continuous at x = 3. For the values of x lesser than 3, we have to select the function f(x) = -x 2 + 4x - 2. lim x->3 - f(x) = lim x->3 - -x 2 + 4x - 2 = -3 2 + 4(3) - 2 = -9 …Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this siteMar 13, 2012 · Finding the probability density function of a function of a continuous random variable 1 Finding cumulative distribution function, given density function using integration Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. ... Continuity of piecewise functions 2. Save Copy.The greatest integer (or floor) function and its graph, seen in calculus and computer science, exhibit similar features. We will take a peek into calculus and preview the related topics of one- and two-sided limits and continuity. Piecewise-defined functions appear frequently in these sections of a calculus course.Learn how to make a piecewise function continuous by finding values for two constants Using the Limit Laws we can prove that given two functions, both continuous on the same interval, then their sum, difference, product, and quotient (where defined) are also continuous on the same interval (where defined). In this section we will work a couple of examples involving limits, continuity and piecewise functions. The Fourier series of f is: a0 + ∞ ∑ n = 1[an ⋅ cos(2nπx L) + bn ⋅ sin(2nπx L)] but we know for obtaining coefficients we have to integrate function from [-T/2,T/2] and intervals are Symmetric but you didn't write that.I have been confused now. I don't think this is necessary to be always true.The short answer: you can just look at (1, 4) ( 1, 4). More formally, recall from the definition of continuity that f f will be continuous at x = 4 x = 4 if: f(4) f ( 4) exists; the limit L =limx→4 f(x) L = lim x → 4 f ( x) exists; and. f(4) = L f ( 4) = L. The limit here doesn't care whether there are other discontinuities; the behaviour ...4. Let f(x) ={ x 3 x x is rational, x is irrational. f ( x) = { x 3 x is rational, x x is irrational. Show that f f is continuous at a ∈R a ∈ R if and only if a = 0 a = 0. My initial approach is to use the sequential criterion with the use of density of rational numbers but I wasn't successful. Any help is much appreciated.This calculus video tutorial explains how to identify points of discontinuity or to prove a function is continuous / discontinuous at a point by using the 3 ...Using the Limit Laws we can prove that given two functions, both continuous on the same interval, then their sum, difference, product, and quotient (where defined) are also continuous on the same interval (where defined). In this section we will work a couple of examples involving limits, continuity and piecewise functions.Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Loading... Explore math with our beautiful ... Continuity of piecewise functions 2. Save Copy. Log InorSign Up. y = 4 ...Continuous addition and multiplication on Euclidean space (dimension > 2) making it into a field? How to select all the vertices on one side of an edge loop? Does an upcast Banishment send the targets to the same place if they share a native plane? Limits of piecewise functions. In this video, we explore limits of piecewise functions using algebraic properties of limits and direct substitution. We learn that to find one-sided and two-sided limits, we need to consider the function definition for the specific interval we're approaching and substitute the value of x accordingly. Feb 7, 2021 · That might be ok if second part, when simplified, turned out to be a function of t2. The factor k/n does not depend on t, so we have. ln((1 +eδt)2/δ) − t. We have ln(ab) = b ln a, so we get: (2/δ) ln(1 +eδt) − t. The power series for ln(1 + x) and exp(x) are well-known, but a little effort is needed to get the series for ln(1 +et), and ... A Function Can be in Pieces. We can create functions that behave differently based on the input (x) value. A function made up of 3 pieces. Example: Imagine a function. when x is less than 2, it gives x2, when x is exactly 2 it gives 6. when x is more than 2 and less than or equal to 6 it gives the line 10−x. It looks like this:A piecewise function may have discontinuities at the boundary points of the function as well as within the functions that make it up. To determine the real numbers for which a piecewise function composed of polynomial functions is not continuous, recall that polynomial functions themselves are continuous on the set of real numbers.👉 Learn how to evaluate the limit of a piecewice function. A piecewise function is a function that has different rules for a different range of values. The ...9.5K. 810K views 6 years ago New Calculus Video Playlist. This calculus review video tutorial explains how to evaluate limits using piecewise functions and how to make a piecewise …This can be applied here, by considering, at each "transition" between one piece of the function to the next, whether the functions composing the part to the right and left of the boundary agree at the boundary.So you have to check the continuity of each component function. Also a general and handy method is to check the continuity of the function using the sequential characterization of continuity in $\mathbb{R}^n,\forall n \geq 1$(and in metric spaces in general). See this.High-functioning depression often goes unnoticed since it tends to affect high-achievers and people who seem fine and happy. Here's a look at the symptoms, causes, risk factors, tr...Plot of the piecewise linear function = {+. In mathematics, a piecewise-defined function (also called a piecewise function, a hybrid function, or definition by cases) is a function whose domain is partitioned into several intervals ("subdomains") on which the function may be defined differently. Piecewise definition is actually a way of specifying the …Calculus with Review. Continuity and the Intermediate Value Theorem. Continuity of piecewise functions. Here we use limits to ensure piecewise functions are …Removable discontinuities occur when a rational function has a factor with an x x that exists in both the numerator and the denominator. Removable discontinuities are shown in a graph by a hollow circle that is also known as a hole. Below is the graph for f(x) = (x+2)(x+1) x+1. f ( x) = ( x + 2) ( x + 1) x + 1.Prove that a function is not differentiable because it's not continuous 7 Prove function is not differentiable even though all directional derivatives exist and it is continuous.Limit properties. (Opens a modal) Limits of combined functions. (Opens a modal) Limits of combined functions: piecewise functions. (Opens a modal) Theorem for limits of …Continuity is a local property which means that if two functions coincide on the neighbourhood of a point, if one of them is continuous in that point, also the other is. In this case you have a function which is the union of two continuous functions on two intervals whose closures do not intersect.Mar 13, 2012 · Finding the probability density function of a function of a continuous random variable 1 Finding cumulative distribution function, given density function using integration In this video I will show you How to Find a and b so that the Piecewise Function is Continuous Everywhere.1. f(x) f ( x) is continuous at x = 4 x = 4 if and only if. limx→4 f(x) = f(4) lim x → 4 f ( x) = f ( 4) In order for the limit to exist, we must have: limx→4− f(x) limx→4−[x2 − 3x] 42 − 3(4) 4 k = limx→4+ f(x) = limx→4+[k + x] = k + 4 = k + 4 = 0 lim x → 4 − f ( x) = lim x → 4 + f ( x) lim x → 4 − [ x 2 − 3 x ...This video goes through one example of how to find a value that will make a piecewise function continuous. This is a typical question in a Calculus Class.#... Learn how to find the values of a and b that make a piecewise function continuous in this calculus video tutorial. You will see examples of how to apply the definition of continuity and the limit ... Find the domain and range of the function f whose graph is shown in Figure 1.2.8. Figure 2.3.8: Graph of a fu