A function f is differentiable at a number a.. A. ... if lim f(x) = f(a), f(z) – f(a) B. ... if lim exists, C. ... if f is defined at a, D. ... if f is continuous at a,

Q: Modify the graphs of the functions ƒ and g as shown to obtain functions that are continuous on 3a,…

A: Given that the graph of functions y=fx and y=gx are given. We have to modify the graphs of the…

Q: f(x) – f(c) If lim exists, it is called the of f at c.

A: We know, If limx→cf(x)-f(c)x-c,exists it is called the derivative of  f at c.Denoted by f'(c)and f…

Q: Sketch the graph of a function f so that... • There is a removable discontinuity at x 3 • There is a…

A: Here is the solution of the given problem.

Q: |x+1| if x + -1 13. Consider the function f(x) = {x² - 1 Evaluate lim f(x). if x = -1 A) - C) DNE B)…

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Q: Let ce (a, b). If ƒ (x) is a function that is continuous at c, then lim,e- [f (x)] = lim,»c+ [f…

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Q: Answer the following True or False: If lim f(x) exists, then f(x) is a differentiable function at x…

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Q: 6. Is it true that the limit of a function lim f(c) = L is the same as evaluating a function f(c)?

A: the limit of a function lim f(c) = L is the same as evaluating a function f(c)

Q: 1 if x<1 1. Consider the function f(x)= . Evaluate lim f(x). if x 21 2х - 3 C) 0 D) 1 A) 2 В) -1

A: Here we have to use the concept of limit.

Q: Which of the following statement/s is/are true about the function whose graph is shown below? A fx)…

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Q: 3. Describe the interval(s) on which the function is continuous. c) S(x)= x-1 2, x= 1

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Q: , if x + -1 -2, if x = -1 Prove that f(x) = {x+1 is continuous at a = -1 by showing the following.…

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Q: If f(x+ y)= f(x)f (y) for all x, y eR and f (x)=1+g(x)G(x), where lim g (x)=0 and lim G (x)…

A: The problem has been solved in detail in the next step.

Q: Let f be a function sati sfying f(x+y)= f(x)f(y)-/4-f(y) for all x, y e R. and lim f(x)= 4. discuss…

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Q: 6. Consider a function f with the following property: if g is any function for which lim g(x) does…

A: One side is not true i have given the contradiction.

Q: Sx² 15 a. Find lim f(x). if x + 2 2. Let f(x) = } if x = 2 X→2 b. Find f(2). Is f(x) continuous at x…

A: Proceed as shown below...

Q: lim 극 et – 1 x-1

A:

Q: 7. Identify if the statement is Always True, Sometimes True or Never True. If lim f(x) exists, then…

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Q: 3. If f is a continuous function, what can you say about lim f(x)?

A: Given thatf is continuous To determinelimx→1f(x)

Q: Suppose that f is a function that is continuous at a number c. Which of the following statements I,…

A: The function f is continuous at a number c.

Q: Which of the following statements about the function y = ƒ(x)graphed here are true, and which are…

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Q: Assume that rs f(x) < 3r. Compute lim f (x)

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Q: Let f(x) be defined on an interval (a,b) and suppose that f(c) #0 at some c where f(x) is…

A: From the definition of continuity we know limx→cf(x)=f(c)f(c) existlimx→cf(x) existsAll of the above…

Q: Which of the following statement/s is/are true about the function whose graph is shown below? fix)…

A: Given the graph of the function f(x). To find which of the following option is/are  correct.

Q: 3. Sketch the graph of a function f such that the following conditions are true: ● f(4) is not…

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