sin h Use the definition of the derivative and the fact that lim cos(h)-1 =1 and lim = 0 to show that if h→0 h h→0 h f(x) = sin x, then f'(x) = cos x. (Hint: sin(a + b) = sin(a) cos(b) + cos(a) sin(b))

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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sin h
Use the definition of the derivative and the fact that lim
cos(h)-1
=1 and lim
= 0 to show that if
h→0
h
h→0 h
f(x) = sin x, then f'(x) = cos x. (Hint: sin(a + b) = sin(a) cos(b) + cos(a) sin(b))
Transcribed Image Text:sin h Use the definition of the derivative and the fact that lim cos(h)-1 =1 and lim = 0 to show that if h→0 h h→0 h f(x) = sin x, then f'(x) = cos x. (Hint: sin(a + b) = sin(a) cos(b) + cos(a) sin(b))
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