Questions from General Calculus


Q: A function h (x) is defined in terms of a

A function h (x) is defined in terms of a differentiable f (x). Find an expression for h(x). h(x) = f (x) / (x2 + 1)

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Q: A cost function C(x) gives the total cost of

A cost function C(x) gives the total cost of producing x units of a product. The elasticity of cost at quantity x, Ec (x), is defined to be the ratio of the relative rate of change of cost (with respe...

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Q: Consider the demand function q = 60,000e-0.

Consider the demand function q = 60,000e-0.5p from Check Your Understanding 5.3. (a) Determine the value of p for which the value of E(p) is 1. For what values of p is demand inelastic? (b) Graph the...

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Q: Find the logarithmic derivative and then determine the percentage rate of change

Find the logarithmic derivative and then determine the percentage rate of change of the function at the point indicated. f (x) = e0.3x at x = 10 and x = 20

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Q: Consider the exponential decay function y = P0e-λt, with

Consider the exponential decay function y = P0e-λt, with time constant T. We define the time to finish to be the time it takes for the function to decay to about 1% of its initial value P0. Show that...

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Q: Find the logarithmic derivative and then determine the percentage rate of change

Find the logarithmic derivative and then determine the percentage rate of change of the function at the point indicated. f (x) = e-0.05x at x = 1 and x = 10

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Q: Find the logarithmic derivative and then determine the percentage rate of change

Find the logarithmic derivative and then determine the percentage rate of change of the function at the point indicated. f (t) = e0.3t2 at t = 1 and t = 5

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Q: Find the logarithmic derivative and then determine the percentage rate of change

Find the logarithmic derivative and then determine the percentage rate of change of the function at the point indicated. G(s) = e-0.05s2 at s = 1 and s = 10

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Q: Find the logarithmic derivative and then determine the percentage rate of change

Find the logarithmic derivative and then determine the percentage rate of change of the function at the point indicated. f (p) = 1/(p + 2) at p = 2 and p = 8

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Q: Find the logarithmic derivative and then determine the percentage rate of change

Find the logarithmic derivative and then determine the percentage rate of change of the function at the point indicated. g(p) = 5/(2p + 3) at p = 1 and p = 11

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