1. Write an equation that expresses the fact that a function f is continuous at the number 4.

Q: Determine the value for k that will make the function continuous at c = 4. x² – 9 if x 4

A: Left-handed limit of a function at a point is obtained by approaching the point from the left on the…

Q: What three conditions must be met for a function ƒ to be continuous at the point (a, b)?

A: Continuity at points: The points of continuity are the points where a function exist and has some…

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

A: Example  f(x)=x4

Q: 1. How to determine whether the function is continuous or not at a certain point?

A: As per our guideline we are supposed to be answer only one question please repost the other question…

Q: Suppose that f(x) 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: 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: When a function is discontinuous at x=2, does that necessarily mean that 2 is not in the domain of…

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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: 1 Suppose that f is a function given as f(x) = 2x -7

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Q: For what value of the constant c is the function f continuous on (-0, 00)? C =

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Q: /Discuss the behavior of the following function as x 0: o,

A: Here, the given function is: f(x)=0,x≥0sin1x,x>0

Q: At what points is the function is continuous y=|2x-1| +4sin(2x)

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Q: Given the following function. - if x2 x > 2 x-2 5, if x = 0 or x = 2 Can f continuous at (-1, ∞)?…

A: Here, for the given function: limx→0-f(x)=limx→01x1+x-1x  (∞-∞…

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: f(x) at x = - 3 X-3

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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: For what value of the constants A and B is the function f continuous on (-∞, ∞)? A√x+6-1 for x 3

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Q: Is the function below continuous at x = -5? f(x)=x3−2x2+5x+1

A: We are to simplify

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: 1. Is the function f(x)= x³ + x−1 even, odd, or neither?

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Q: What is the value "L", if exists, when a variable "x" in f(x) approaches a certain number "d" in the…

A: Given: A function fx is given. To Find: What is the value "L", if exists, when a variable "x" in…

Q: Determine whether  the following statement is true or false, and explain why. If ƒ″(x) > 0 on an…

A: If the second derivative of a function f(x) is defined on an interval (a,b) and f ''(x) > 0 on…

Q: Find the value of k, if the constant k that makes the function continuous:

A: Given,          f(x)=x2+k2if x≤4kx+12if x>4

Q: When is a function of two (three) independent variables continuous at a point in its domain? Give…

A: When is a function of two (three) independent variables continuousat a point in its domain? Give…

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: where is the function f(x)= llxll-2 continuous (or discontinuous)?

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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: What does it mean for a function to be left-continuous at a point?

A: function to be left-continuous at a point?

Q: At what points are the functions continuous?

A: The part of the function -x2 / 2 is always continuous. There is no point of discontinuity here. The…

Q: en the function f(x)= – (x+4)3, which of the following statement talks about its relative and…

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Q: Is the function given by f(x)=x^2+3x/2x-1 continuous over its domain?

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Q: Determine where the function f(x) is continuous. f(x) = /2-x

A: We have to determine where th function f(x)=(2-x)^(1/3) is continuous

Q: When can we say that a function is continuous at a number?

A: To explain: The continuity of a function at a point.

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

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

Q: Solve for a andb that makes the function continuous at every number in its domain f(x) = 2x+1 x5

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Q: Give the three conditions that must be satisfied by a function to be continuous at a point.

A: We have to write  the three conditions that must be satisfied by a function to be continuous at a…

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: Explain if the function is continuous or not for the given number a. if x>1 if x = 1 ,a=1 if x<1…

A: we have given function     we need to determine the continuity at a=1

Q: Construct a function that is undefined at points 2,3 and T.

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Q: Find the value of a and b that will make the function continuous. for x 1/2

A: The function f(x)=1x,        for x&lt;-1ax+b,  for  -1≤x≤121x,         for x&gt;12. We have to find…

Q: A function has a zero at X = 8, indicating what?

A: Given, A function has a zero at X=8

Q: In what degree of homogeneity is the function x + 4y

A: The given function is x+4y To find: degree of homogeneity of the given function.

Q: Determine whether the following function is continuous at the given point x = 3x2 + 14x – 5 1 | f(x)…

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Q: Give the graph or the formula of a function that is continuous but not differentiable at x=0.

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Q: Which of the following does not represent a function that is continuous everywhere?

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Q: Is the function continuous from X = -5 to x = 0? This function is made up of four (4) linear…

A: 1. True, the function is continous from x=-5 to x=0 as there is no break in the       graph between…

Q: In calculus was claimed  that increasing (or decreasing ) functions  defined on a single interval is…

A: Consider a one - to - one function in an fixed interval.  For the function f(x), in the interval 0…

Q: if x1

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Q: A function is defined as: (-1 for - 3<x< 0 %3D +1 for 0 < x < 3

A: Given, f(x)=-1    for  -3≤x&lt;0+1    for    0&lt;x≤3 Given function is a piecewise defined…

Q: Select all of the graphs that depict a function which is not differentiable at x=0.

A: Here, we need to select all the graphs that depict a function which is not differentiable at x=0.…

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.