Suppose f and g have Taylor series about the point a. a. If f(a) = g(a) =

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Suppose f and g have Taylor series about the point a. 

a. If f(a) = g(a) = 0 and g'(a) ≠ 0, evaluate |lim f(x)/g(x) |x>a by expanding f and g in their Taylor series. Show that the result is consistent with l’Hôpital’s Rule.

b. If f(a) = g(a) = f'(a) = g'(a) = 0 and g"(a) ≠ 0, evaluate f(x) lim x→a g(x) by expanding f and g in their Taylor series. Show that the result is consistent with two applications of l’Hôpital’s Rule.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

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

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