89. Let f be a continuous function for all real numbers. Let g be the function defined by g(x) = [¨ s(t) dt. If the average rate of change of g on the interval 25x5 5 is 6, which of the following statements must be true? (A) The average value of f on the interval 2 < x S 5 is 6. (B) gʻ(2) = 6 g'(5) + g'(2) (C) 2

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A:

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A: Explained below

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A: Given f(x) is continuous and differentiable and f(3) = f(s) = 2Concept Roll's Theorem If f(x) is…

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Q: 4. Consider the function f(x) = Vx – I (a) Use the limit definition of derivative to find f'(x)

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Q: 16 8 If f is continuous and f(x) dx = 10, find f(2x) dx.

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Q: 19. Determine the following function if continuous at 2 f(x) = (,) ;at x = -1 + 1 A. discontinuous…

A: Explanation of the answer is as follows

Q: 9. Suppose for sume funchion f we have its derivative, f'x) = e*sin(x), on the %3D interval o< x<…

A: We can use application of derivative in order to solve the given problem.

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Q: 51. Is the function given by G(x) 1 continuous at x = 0? Why or why not?

A: Given: Gx=1x To check whether the given function is continuous at x=0

Q: 6-Iff is a continuous at x=c, then f has a derivative at x=c. * a. True b. False

A: Consider the given statement "If f is a continuous at x = c, then f has a derivative at x = c".

Q: If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

A: The detailed solution is as follows below:

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A: In the given question, f(x) is cos(x) and a is 9π

Q: 4. Consider the function f(x) = Vx – 1 (a) Use the limit definition of derivative to find f'(x)

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Q: 57. Is the function given by Sx + 1, for x 4, g(x) = continuous at x = 4? Why or why not?

A: gx=12x+1,   for  x&lt;4-x+7,   for  x&gt;4 Now left hand limit at x=4 is, limx→4-fx=limx→4-12x+1…

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Q: 49. Is the function given by g(x) = x² 3x continuous at x = 4? Why or why not?

A: Given: g(x)=x2-3x Determine the limit at x=4. limx→4g(x)=limx→4(x2-3x)

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Q: Suppose g: IR - IR is a differentiable function with bounded derivative, Fix e> 0 , and define flx)…

A: to show f is one one we will show that for  x1 not equals to x2 , f(x1) is not f(x2)

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A: Given statement : Let y=f(x) be a differentiable function. If the derivative of f is zero at x=a,…

Q: 4). If f(1) = 12 and f' is continuous and | f'(x) dx=17, what is the value of f(4)?

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Q: 16. Show that f(x) = Vx - 2 is continuous at x=2 but not differentiable at x=2.

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Q: 56. Is the function given by Sx + 1, for x 4, G(x) = continuous at x = 4? Why or why not?

A: As we know that  Function will be continuous at x=a if limx→a-fx=limx→a+fx=fa

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Q: 4). If f(1) = 12 and f' is continuous and f'(x) dx=17, what is the value of f(4)?

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Q: question. sf continuous at x = - 3? AY 5- 4- 3- 20 -5 -4 3 -2 -14 123 4 5 -2- -3- -4- -5-

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A: Hi there, i have explain that if x tends to 1 from right side the function will give +1 and while…

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Q: Consider the function fcx) = (メフチ 5 E- xet X if x >5 if メ=5 5-X S> X f! Is fe) continuous at x=5?…

A: NOTE: Refresh your page if you can't see any equations. .

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A: fx is continuous and differentiable function on the interval -7, 0, f-7=-3 &amp; f'x≤2.

Q: 3 Find f(x) if f(1) = 1 and the tangent line at (x, f(x)) has slope f(x) =

A: on solving this we get the

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A: This is absolute function then we need to find piece wise function

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Q: 43 31) Describe all y=flx) which are defìned for all XEIR and satisfy continuoUs functions ə47…

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