Use the asymptotic behaviour of f = sin(πx) + xe^−x to sketch its graph. Include the graphs of y = xe^−x and y = sin(πx) and discuss the behaviour of the graph of f relative to these two graphs.

Q: Apply the rules of derivatives to find the ? ′ (?) for ?(?) = sec2 ? ∙ tan3 ?.   Please show all…

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Q: (5x) S sin(x) tan(x) .........

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Q: f (x) = 2x + 2/2 cos (x) For what values of x does the graph of f have a horizontal tangent?

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Q: Graph of f" +x 8. The graph of f", the second derivative of the function f, is shown above. Which of…

A: Step 1:Step 2:Step 3: Step 4:

Q: Given the graph of the function f below. Which of the following has the highest value? f'(-2) f' (})…

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Q: (a) Select inflection points if the graph shows f (x). (b) Select inflection points if the graph…

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Q: Find fi( using the derivative rules tanx y2-3

A: Given, the function is                         We have to find the derivative of this function i.e.…

Q: Write the equation of the tangent and normal lines to f(x) at x – 1 x = = 4.

A: Consider the given function fx=x+1x-1 at x = 4. Tangent line: Obtain the y-coordinate of the point…

Q: For a function g, we are given that g(-6) = -8 and g'(-6) = 3. What's the equation of the tangent…

A: For a function , we are given that  and .To find the equation of the tangent line to the graph of…

Q: y=/(x) -3 -1 3. ****

A: Given , the graph of                            y=f(x)

Q: Using the graph of the function † (x) given beloW, determine the sign for each of the following.…

A: Explanation of the answer is as follows

Q: Find the derivative of each of the following functions. No simplification required. • f(x) =…

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Q: What transformation is required to obtain the graph of the function f(x) = 8cosx from the graph of…

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Q: Sketch a function where ?′(?) > 0  and ?′′(?) > 0 always and passes through the point (0,1).

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Q: tan a 5 f(x) = sec a find f' (x). Find f'().

A: We have to find the derivative of the given function

Q: If possible please answer all questions. Find the derivative:  1) y=cos-1(1/x) 2)?=cot-1(√x-1) 3)…

A: Find the derivatives

Q: Find the equation of all its vertical asymptotes given the cosecant function y = csc 2 csc-) 3.

A: The given function is y=cscx2-π3. Obtain the vertical asymptotes by solving sinx2-π3=0 as follows.

Q: Given the graph of y = f(x) sketch the graph of f'(x) 2 -2 -2

A: Given: The graph of fx as follows:   To sketch: The graph of f'x

Q: Graph of f" +x 8. The graph of f", the second derivative of the function f, is shown above. Which of…

A: Step 1:On the interval where f"x<0   the function  should be concave down   and  on  the…

Q: 2. Below is the graph of a function f(x). On the same set of axes or to the right, draw a rough…

A: Graph of f'(x)

Q: Plot the following function 0 <x< T sin(x) f(x) = } -0.81x2 + 7.64x – 16 π<x< 2π -1.62x2 + 25.46x –…

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Q: Sketch the graph of each tangent curve in the interval from 0 to 2n and give the period of the…

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