3. Consider the function A(x) = f cost sin³ tdt for x in [0, 2π]. Calculate A'(x), determine the intervals of increase/decrease and the critical points of A on (0, 27), if they exist. • Compute A(). • Sketch the graph of A on [0, 2π] using the above computation and the following information: A"(x) < 0 if and only if x in [0, ) U (2, 4) U (5,2π].

Q: 3. Sketch the graph of a function that satisfies all of the given conditions. • f'(0) = f'(2) = 0 •…

A: THE EXPLANATION HAS BEEN GIVEN IN THE ATTACHED FILE.

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Q: c. List any critical values. d. Identify intervals of increase. e. Identify intervals of decrease.

A:

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A:

Q: \lim_(x->\infty )(e^(-x)+2cos 3x)

A: See the answer below

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A: f''(x)=8x +6integrating w.r.t. x;∫ f''(x) dx =f'(x)f'(x) =∫ (8x+6) dx        =8x22+6x+Cf'(x)…

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A: for part a see 2nd step. for part b see 3rd step.

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Q: 12 If f(t) = find f'(t). f'(t) =

A:

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Q: ) Given the function f(x) derivative f"(1) with h, h/2 and h/4. 5. e Vx cos (Tx), approximate the…

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A: Given , to determine the x-value where  a relative maximum exists  for .