When a function is discontinuous at x=2, does that necessarily mean that 2 is not in the domain of f?

Q: f(x) = In(x)

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Q: Give a function that does not have an inflection point at a pointwhere f ″(x) = 0.

A: Example  f(x)=x4

Q: Show that the function has a removable discontinuity at x = 4.

A: A function is continuous at a point x=a if limx→af(x)=f(a). For limit at a point to exist both…

Q: Is there a real function f(x) that is differentiable only at a point x?

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Q: Sketch the graph of the function f(x). f(x) is continuous from the right at x = 3, but not from the…

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Q: Evaluate the piecewise-defined function at the indicated values. x² if x 0 f(-2) f(0)

A: f(-2)=4 f(0)=1

Q: - Find and classify the discontinuities of the function f(x) x2 - 1

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Q: Define f(x) = (x2 - 81)/(x - 9) at x = 9 so that the function becomes continuous at 9.

A: Concept: A definition of a function is that a relation from a set of inputs to a set of possible…

Q: Given selected values of the twice-differentiable function f, which of the following choices could…

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Q: Define f(x) =(x2 - 81)/(x - 9)at x = 9 so that the function becomes continuous at 9.

A: Given function is fx=x2-81x-9. To define function fxso that the function becomes continuous at x=9.…

Q: but f'(x) is never equal to 0. Why

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Q: The function is discontinuous at x= -4. At this point, is f continuous from the right, left, or…

A: A function f is said to be right continuous at a point a if it is defined on an interval and if…

Q: Use the given graph of the function to find the r-values for which f is not differentiable.

A: The function fx is not differentiable at any point x=c, in the following cases, 1) fx is not…

Q: For which values of x is the function below NOT continuous?

A: To find out the values of x at which the function is discontinuous.

Q: On what domain is the function f(x)=1+√−6−3x continuous?

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Q: x, if -1くx<

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Q: Suppose that flx) is a differentiable function and g(x)=(x+2)/f(x). If f(0)= 22 and f(0)=5, then…

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Q: when x # 1 Show that f(x)% = 2 when x =1 is discontinuous at x 1

A: Given query is to find the continuity of the function at x = 1.

Q: What type of discontinuity occurs at x = 1 for the piecewise function? if x <1 if 1<x 3+ x h(x) =…

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Q: What type of discontinuity does the function f(x)=xsecx have?

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Q: Let ƒ be the function given by ƒ(x) = (x-2)²(x+3). For what values of x is f not continuous?

A: The given function is fx=(x-2)2·(x+3)(x-2)·(x+1) We have to find the values of x, for which f is not…

Q: The graph of the function f is given below. f is not differentiable at

A: For differentiability of a function,  Left hand derivative = Right hand derivative  That is :

Q: Suppose that f(x) is a differentiable function and g(x)=(x+2)/f(x). If f(1)= 5 and f'(1)=10, then…

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Q: Explain why the function is discontinuous at the given number a. f(x) = {* 2* x + 3 _ifx -1 a = -1

A: For continuity left hand limit and right hand limit should be same if not then function will be…

Q: How would you "remove the discontinuity" of f? In other words, how would you define f(3) in order to…

A: The given function is: f(x)=x2-x-6x-3

Q: Let f(x)=x^3-4x^2. Find the points on the graph of f where the tangent line is horizontal.

A: f(x) = x3 - 4x2Horizontal tangent when f'(x) = 0differentiate f(x) with respect to 'x'f'(x) = 3x2 -…

Q: On what domain is the function f(x)=x^2+7x−6 continuous?

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Q: Explain why the function is discontinuous at x = 1. f(x) = (3 Зх for x 1

A: We have to find the left and right-hand limit of f(x) at x=1 So the right and left hand limits are…

Q: Use Intermediate Vaule Tun to show that the functions f(x) = x^3 and g(x) = 2x + 3 intersect at at…

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Q: Find the intervals on which the graph of f is concave upward. f(x) = In (x² – 2x + 10)

A: f(x)= In(x2 - 2x + 10) To find the intervals on which the graph of f is concave upward.

Q: Show that the function is discontinuous on R. f(x) = { 1; 0; for x € Q for a Q

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Q: On what domain is the function f(x) = 3x + 5x + 6 continuous?

A: The given function is, fx=3x2+5x+6

Q: For the function f, how would you remove the discontinuity? In other words, how would you define…

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Q: Determine if the given function is differentiable at a = 1 4 – 2x, if x 1

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Q: Examine whether or not the function (4-x² f (x) =- [4+x if x0 Is continuous at x = 0

A: Check whether limx→0f(x) = limx→0(4-x2) and limx→0(4+x), if both sides are equal then it is…

Q: X+1 5) Is the function given by f(x) x2 - 8x + 15 continuous at x = 3? Why or why not?

A: f(x)=x+1x2-8x+15

Q: Explain why the function h is discontinuous at a = -2. 1 x = -2 h(x) = x + 2 1 x = -2

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: If f (x)= x2 - 4x, at which point on the graph f (x) is the tangent line horizontal

A: topic - slope of tangent line

Q: Determine if the function is continuous or discontinuous at x=2. h(x) = x - 1, if x 22 2x- 1, if x<2…

A: if Left hand limit and right hand limit are equal then function is…

Q: function

A: We are given a function : f(x)=x2-2x+2x-3 We have to determine the domain of given function where…

Q: Find a value of the constant k, if possible, that will make the function continuous everywhere. (kx…

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Q: Show that if f(x)  = x4 , then  f"(0)  =0, but  (0, 0)is not aninflection point of the graph of f.

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Q: Given that f(x) = 5x – 13 where f(x) = y, define a function rule for f-1.

A: Given function, fx=5x-13 The objective is to find the inverse function. y=fx⇒f-1y=x The following…

Q: Use the given graph of the function to find the x-values for which f is differentiable. not 1,0

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Q: For the function f(x)=3x", evaluale : f(Xth)=

A: F(x) = 3x2 , put x = x+h                                                            F(x+h) =3(x+h)2…

Q: if x1

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Q: Which of the following functions passes through the point (0,12) and satisfies f'(x)=8 ?

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Q: 3 Show that the function f(x) = Vx – 5 is one to one function.

A: The given function is: fx=x-53