Questions from General Calculus


Q: Let g (x) = f 9x2), where f is

Let g (x) = f 9x2), where f is twice differentiable for all x, f'(x) > 0 for all x ≠ 0, and f is concave downward on (-∞, 0) and concave upward on (0, ∞). (a). At what numbers does g have an extreme v...

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Q: The Fresnel function was defined in Example 4 and graphed in Figures

The Fresnel function was defined in Example 4 and graphed in Figures 6 and 7. Figures 6: Figures 7: (a). At what values of does this function have local maxi mum values? (b). On what intervals is...

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Q: Graph the function f (x) = cos2x sin3x and use

Graph the function f (x) = cos2x sin3x and use the graph to guess the value of the integral f2π0f (x) dx. Then evaluate the integral to confirm your guess.

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Q: Find the derivative of the function. F (x)

Find the derivative of the function. F (x) = fx0t2/1 + t2, dt

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Q: Evaluate the integral. f 10/ (x – 1

Evaluate the integral. f 10/ (x – 1) (x2 + 9), dx

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Q: Express as a definite integral on the interval [0, π

Express as a definite integral on the interval [0, π] and then evaluate the integral.

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Q: If f60f (x) dx = 10 and f40f (x

If f60f (x) dx = 10 and f40f (x) dx = 4, find f64f (x) dx.

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Q: (a). Write f20e3x dx as a limit of Riemann sums

(a). Write f20e3x dx as a limit of Riemann sums, taking the sample points to be right endpoints. Use a computer algebra system to evaluate the sum and to compute the limit. (b). Use the Evaluation The...

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Q: Set up, but do not evaluate, an integral for the

Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

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Q: (a). Find the vertical and horizontal asymptotes, if any

(a). Find the vertical and horizontal asymptotes, if any. (b). Find the intervals of increase or decrease. (c). Find the local maximum and minimum values. (d). Find the intervals of concavity and the...

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