Questions from General Calculus


Q: If g (x) = f (f (x)),

If g (x) = f (f (x)), use the table to estimate the value of g'(1).

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Q: Suppose f is differentiable on R. Let F (x)

Suppose f is differentiable on R. Let F (x) = f (ex) and G (x) = ef(x). Find expressions for (a) F'(x) and (b) G'(x).

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Q: A manufacturer produces bolts of a fabric with a fixed width.

A manufacturer produces bolts of a fabric with a fixed width. The quantity q of this fabric (measured in yards) that is sold is a function of the selling price p (in dollars per yard), so we can write...

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Q: Suppose f is differentiable on R and a is a real number

Suppose f is differentiable on R and a is a real number. Let F (x) = f (xa) and G (x) = [f (x)]a. Find expressions for (a) F'(x) and (b) G'(x).

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Q: Let r (x) = f (g (h (

Let r (x) = f (g (h (x))), where h (1) = 2, g (2) = 3, h'(1) = 4, g'(2) = 5, and f'(3) = 6. Find r'(1).

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Q: If g is a twice differentiable function and f (x)

If g is a twice differentiable function and f (x) = xg (x2), find f" in terms of g, g', and g".

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Q: If F (x) = f (3f (4f (

If F (x) = f (3f (4f (x))), where f (0) = 0 and f'(0) = 2, find F'(0).

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Q: If F (x) = f (xf (xf (

If F (x) = f (xf (xf (x))), where f (1) = 2, f (2) = 3, f'(1) = 4, f'(2) = 5, and f'(3) = 6, find F'(1).

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Q: Show that the function y = e2x (A cos 3x +

Show that the function y = e2x (A cos 3x + B sin 3x) satisfies the differential equation y" – 4y' + 13y = 0.

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Q: For what values of r does the function y = erx satisfy

For what values of r does the function y = erx satisfy the differential equation y" – 4y' + y = 0?

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