Use a graph to determine whether the given function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity. |x[ if x + 0 h(x) : if x = 0 O Continuous on its domain. O discontinuity at x=0

Q: a) Is f(x) continuous at x=2? Explain. b) What is the type of discontinuity of f(x)? c) On what open…

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Q: Find each x-value at which f is discontinuous and for each x-value, determine whether f is…

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Q: Is the following function continuous over all real values of 'x'? If applicable identify any…

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Q: Let f(x) = – and let g be the function defined by (x – 3)(x – 5) if x 3 (a) Evaluate lim(ƒ o g)(x).…

A: Ans:-  a) - infinity  b) infinite discontinuity  Explanations:- In part (b) as LHL is not equal to…

Q: Determine if the function is continuous at the specified point. If it is discontinuous, what type of…

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Q: f(x)={-2x, X = x ≤ 4 x>4 x² - 8x + 5, Find the x-value at which f is not continuous. Is the…

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Q: x2 – 1 f (x) ; x = 1 х — 1

A: We will solve the following

Q: Find each x-value at which f is discontinuous and for each x-value, determine whether f is…

A: Check for the discontinuity at x = 1.

Q: Use the IVT to show that if f is continuous and one-to-one on an interval [a, b], then f is either…

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Q: find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?

A: A rational function is said to be discontinuous if the denominator expression becomes zero for any…

Q: Determine using the given graph if the function f is continuous on the following intervals. 2. 1. a.…

A: Let's find.

Q: S(x + 4)² -2 < x x < -2 f(x)

A: fx=x+42    -2≤xx2              x&lt;-2 Since the given function is a polynomial function for all…

Q: Consider the function x - 3 for x4 By using the characterization of continuous function in terms of…

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Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?

A: Given: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are…

Q: Determine whether a function is continuous at a given number. If it is discontinuous, identify which…

A: Given function f(x) = -2x +3  for x≤1   and f(x) = x2  for  x &gt; 1

Q: 1 f (x) = 3 %3D х — 3

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Q: Determine if the given function is continuous at x=a, if the function is continuous, then determine…

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Q: Determine whether a function is continuous at a given number. If it is discontinuous, identify which…

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Q: find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?

A: Given: find the x-values (if any) at which f is not continuous. Which of the discontinuities are…

Q: say whether the function graphed is continuous on[-1, 3]. If not, where does it fail to be…

A: The graph of a function is said to be continuous in an interval if there is no break in ite graph at…

Q: Give an example of functions f and g such that f (g(x)) is continuous but g has at least one…

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Q: Explain if the function is continuous or not for the given number a. if x > 1 f(x) = {1 if x = 1…

A: topic - limits and continuity

Q: Determine whether a function is continuous at a given number. If it is discontinuous, identify which…

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Q: { -2x + 3 x 1

A: We have given a piecewise define a function fx which definition change at x=1. The functions…

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?

A: f(x)=x+2x2-3x-10 Finding the x value at which function is not continuous .  And which of the…

Q: Assume whether the function graphed in the accompanying figure is continuous on [-1,3]. y = k(x) 2 3

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Q: Determine if the following is continuous at the indicated value of x. If it is continuous determine…

A: Given that: f(x)=|3x-5|,    if -5≤x≤-14xx-1,        if  -1&lt;x≤5     NOTE: As per our answering…

Q: Determine whether a function is continuous at a given number. If it is discontinuous, identify which…

A: Discontinuity of the First Kind: Function f(x) is said to have a discontinuity of the first kind…

Q: The graph of a function f is given. y 1 1 Determine whether fis continuous on its domain.

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Q: say whether the function graphed is continuous on[-1, 3]. If not, where does it fail to be…

A: It is clear from graph of y=k(x) , that the function k(x) is continuous on the interval [-1,1) and…

Q: Use a graph to determine whether the function is continuous on its domain. If it is not continuous…

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Q: Determine using the given graph if the function f is continuous on the following intervals. 1. a.…

A: A real valued function f(x) is defined in an interval,say [a,b] and its graph is available to…

Q: consider the function g(x) =   2 − πx         if x ≤ a               x^4              if x > a…

A: We are given the following function. We need to find a value of a. Idea: We will find the value of…

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?…

A: f(x) = x4 − 81x is a polynomial function.

Q: Let f(x) = and let g be the function defined by %3D (x – 3)(x – 5) if x 3 () Evaluate li (b) Is ƒ…

A: We have to find

Q: Determine if the given function is continuous at a given value of x.

A: This question is related to limits and continuity, we will solve it using given information.

Q: Is f continuous at x = 2?

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Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Determine whether a function is continuous at a given number. If it is discontinuous, identify which…

A: Given,

Q: Determine if the given function is continuous on each of the given intervals. x - 1 f(x) = {2x2 - 3x…

A: Consider the function  f(x)=x-1             ,       x≤02x2-3x+1   ,       0&lt;x≤23x3-x2         ,…

Q: Find each x-value at which f is discontinuous and for each x-value, determine whether f is…

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Q: a, determine if the discontinuity is removable or essential. 1+ x, x 2 1. H(x) = }2 – x,

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: а. Determine the discontinuities of the following functions and state why the function fails to be…

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Q: determine whether or not the function is continuous at the indicatedpoint. If not, determine whether…

A: Let’s  verify for continuity at x=1As we know by definition of abs |x| function

Q: Determine the discontinuities of the following functions and state why the function fails to be…

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Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?

A: Given f(x)=2x-3x-3

Q: say whether the function graphed is continuous on[-1, 3]. If not, where does it fail to be…

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Q: -x, x±1 f(x) = 0, x= 1

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Q: r² + 5x , if x -5 x – 5

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.