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
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).
Transcribed Image Text:
f(v) – f(u) - f'(u) if v # u H(v) if v = u. lim H(v) = 0.
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Related Book For
Calculus Early Transcendentals
ISBN: 978-0321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
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