Let f and g be differentiable functions with h(x) = f(g(x)). For a given constant a, let

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Let f and g be differentiable functions with h(x) = f(g(x)). For a given constant a, let u = g(a) and v = g(x), and define

f(v) – f(u) - f'(u) if v # u H(v) if v = u.

a. Show thatlim H(v) = 0.

b. For any value of u show that

f(v) - f(u) = (H(v) + f'(u))(v - u).

c. Show that

d. Show that h'(a) = f'(g(a))g'(a).

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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