Let h(x) = f(x) + g(x). If f(x) = 2x² and g(x) = 8x5, what is h'(x)? Do not include "h' (x) =" in your answer. For example, if you found h'(x) = 5x² + 1, you would enter 5x² + 1. Provide your answer below:

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A: The graph of the function is  To evaluate:  1. limx→1+fx2. limx→4-fx3. limx→4+fx4. limx→1-fx5.…

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

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A: Topic:- function and limits and continuity

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A: To prove the identity.

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A: Here is the solution:

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A: Please see the below picture for detailed solution.

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

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A: See the details solution in below

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A: Topic: application of integration and differential equations

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A: we have f(x,y) = xlnx -ylny

Q: What is the coordinates of the point on the line y = 2x +1 which is closest to the point (2, 1)?

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

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Q: 4. Find f '(0.5) for f(x) = [Arc tan(t)dt - Arc ta O 0.8 0.131 O 0.120 O 0.464

A: The function fx is given by fx = ∫0xArctantdt To evaluate: The value of f'0.5

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A:

Q: 15. Let 2 √x 4 3/2 y' = 2y + 2xy' 13/2 Solve for y' when x = 1 and y = 4

A: NOTE: Refresh your page if you can't see any equations. . here we have x=1 and y=4

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Q: x-2 lim x-2 √2x2+1-3

A: Given,            limx→2x-22x2+1-3