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 a Show that 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) f(v) f(u) f'(u) if v u H(v) if v u lim H(v) 0 ...

a b Suppose u v Then clearly both sides of the gi ...

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

Question:

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

Question:

f(v) – f(u) - f'(u) if v # u H(v) if v = u. lim H(v) = 0.

Step by Step Answer:

a b Suppose u v Then clearly both sides of the gi...View the full answer

Calculus Early Transcendentals

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