A function f(x) is said to have a removable discontinuity at x = a if: 1. f is either not defined or not continuous at x = a. 2. f(a) could either be defined or redefined so that the new function IS continuous at x = a. Let 4 - 3x + 20 if x + 0 and x + 5 x ( x – 5) f(x) = 4 | if x = 0 Show that f(x) has a removable discontinuity at 0 and determine what value for f(0) would make f(x) continuous at x = 0. Must redefine f(0) Hint: Try combining the fractions and simplifying. The discontinuity at x = removable discontinuity, just in case you were wondering. 5 is actually NOT a

Q: B) Test the functions continuity at the given poihts: (x²-x-6 1) f(x) 3D x * 3 ,at x 3, x 5 X-3 x =…

A: f(x)=x2-x-6x-3x≠35x=3

Q: DETERMINE WHETHER THE GIVEN FUNCTION m(x) IS CONTINUOUS OR DISCONTINUOUS AT x = -1

A: NOTE: Refresh your page if you can't see any equations. . find the left-hand limit of the function…

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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: 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…

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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.…

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A: We have to factor the numerator  At x=3 both of the numerator and denominator are zero, so we get…

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Q: A function f(x) is said to have a removable discontinuity at x = 1. f is either not defined or not…

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Q: A function f(x) is said to have a removable discontinuity at = a if: 1. f is either not defined or…

A: The given function is f(x)=2x2+3x-5x-1

Q: Question 26

A: To determine the domian of the function.

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Q: Find c so that f is continuous at every point f(x) = 5x+12c, if x < -5 f(x) = (cx^2)+1, if x ≥ -5

A: Given- fx=5x+12c if x&lt;-5cx2+1   if x≥-5 To find- The value of c that  the above function is…

Q: A function f(x) is said to have a removable discontinuity at a a if: 1. f is either not defined or…

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Q: A function f(x) is said to have a removable discontinuity at x = a if: 1. f is either not defined or…

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Q: Given f(x) is a continuous function. If f( – 5) = 1 and f'(x) > 4 for – 5 <x < 2, what is the…

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Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A: Given the functionfx=x2+2xx≤14-x1&lt;x&lt;3x-3x≥3we discuss about the discontinuity of the…

Q: | if x#3 6. %3D 15. Show that if the function g is defined by g(x) = if x=3 then g is not continuous…

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Q: 11. Let g(x) be a continuous function for all x € R. If f'(x) = g(x)f(x) for all x e R, find f(x).…

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Q: Letf be a function defined below. x² + 3x] if xS0,x = 3 f(x) = || x+ 3 x+1 if T >x>0 x21 if Discuss…

A: The function is not defined at the point x=-3 . Hence the function is not continuous at the point…

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Q: 27. A function on [0,2] defined by f(x) = -x² |5x – 4 4x³ 3x (3x + 4 - if x ≤ 0 if 0 < x≤ 1 1<x<2 if…

A:

Q: 19. Suppose f is a piecewise-defined function, equal to g(x) if x 2, where g and h are contin- uous…

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Q: 1. Determine where each of the following functions are continuous. x2 - 3x - 10 a. f(x) = %3D x2 -…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A function f(x) is said to have a removable discontinuity at `x-a` if: 1. ` f' is either not defined…

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

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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

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Q: 3x if x 2

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A: In order to solve the given question equate the left hand limit and the right hand limit as the…

Q: Sketch the graph of a continuous function y =f(x) that satisfies the following conditions: 1. f'(x)…

A: This question is about graphing a function

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

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Q: 2. Determine whether f is continuous or discontinuous at 1. (x – 1 if x > 1 f(x) -x² if x <1 O f is…

A: Given query is to find function is continuous or not at x = 1.

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Q: Consider the function f with domain (-2, : 3|22 – 1| if – 2 < x < 1 2x2 + 2x – 4 f(x) = 3 if x = 1…

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Q: B. Determine whether f(x) (x - 3) (2x + 1) (x + 4) is continuous at x= 3.

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Q: A function f(x) is said to have a removable discontinuity at x = a if: 1. f is either not defined or…

A: Here is the solution:

Q: Consider the function f with domain (-2, ∞): 3|22 – 1| if – 2 < x < 1 2x2 + 2х — 4 f(x) = 3 if x = 1…

A: Solution is given below:

Q: A function f(x) is said to have a removable discontinuity at a = a if: 1. f is either not defined or…

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Q: ((4— х)2 х 1 continuity at the indicated test point. If it is discontinuous, specify the type of…

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Q: 6. For each piecewise function f(x), determine whether f(x) is continuous at each of its breakpoint.…

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Q: (b) Suppose that f(x) = ൜βx2 − 3    if x ≤ 2βx + 2      if x &gt; 2 Find the value of β so that f(x)…

A: For continuity, left hand limit=right hand limit=f(x)

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A: Given function is, f'x=1x2+fx2 The above equation f'x is always positive which means fx  is always…

Q: (b) Suppose that f(x) =  βx2 − 3            if x ≤ 2 βx + 2             if x > 2 Find the value of β…

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Q: Let f(x) = 2x² + 5x - 7 x-1 = 1 and determine what value for f(1) would make Show that f(x) has a…

A: Solution of given question is written in below steps.

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.