10. Given f(x) > 0 with f '(x) < 0, and f "(x) > 0 for all x in the interval [0, 2] with f(0) = 1 and f(2)= 0.2, the left, right, trapezoidal, and midpoint rule approximations were used to estimate = {f(x)dx. The estimates were 0.7811, 0.8675, 0.8650, 0.8632 and 0.9540, and the same number of subintervals were used in each case. Match the rule to its estimate. 1. left endpoint 2. actual area 3. trapezoidal 4. midpoint 5. right endpoint a. 0.9540 b. 0.7811 c. 0.8632 d. 0.8675 e. 0.8650

Q: 8. Find f'(x) for the function f (x) = (5x² + 3)4

A: ddxfxn=nfxn-1f'x

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A:

Q: 81. Let f be a function with derivative given by f'(x)=√x3+1. What is the length of the graph of y =…

A: If you have any questions let me know in comment box thankyou for your question.

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A: To find f'(2)

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A: given f''(x)=5x+1f'(-1)=-5  and f(-1)=0we know ∫xndx=xn+1n+1+c

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A:

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Q: 11. f(x) = 4x³ In(5x² +1)

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A:

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A: We will differentiate f twice and then evaluate at x = 0 and at x = 4

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A:

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A: 2) The fx isfx=xex

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A: