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92. Constant Rule proof For the constant function f(x) = c, use the definition of the derivative to show that f'(x) = 0.

92. Constant Rule proof For the constant function f(x) = c, use the definition of the derivative to show that f'(x) = 0.

Calculus: Early Transcendentals
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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Question 92?
89-91. Calculator limits Use a calculator to approximate the following limits. e³x - 1 89. T lim x-0 90. lim 1 n x 91. lim XX +0x X n n 92. Constant Rule proof For the constant function f(x) = c, use the definition of the derivative to show that f'(x) = 0. 93. Alternative proof of the Power Rule The Binomial Theorem states that for any positive integer n, (a+b)" = a + na"-¹b+ n(n − 1) 2.1 an-26² + - n(n − 1) (n − 2) 3.2.1 f(x+h)-f(x) h Use this formula and the definition f'(x) = lim h→0 d show that that -(x) = nxn-1, for any positive integer n. dx -an-38³ +...+ to
Transcribed Image Text:89-91. Calculator limits Use a calculator to approximate the following limits. e³x - 1 89. T lim x-0 90. lim 1 n x 91. lim XX +0x X n n 92. Constant Rule proof For the constant function f(x) = c, use the definition of the derivative to show that f'(x) = 0. 93. Alternative proof of the Power Rule The Binomial Theorem states that for any positive integer n, (a+b)" = a + na"-¹b+ n(n − 1) 2.1 an-26² + - n(n − 1) (n − 2) 3.2.1 f(x+h)-f(x) h Use this formula and the definition f'(x) = lim h→0 d show that that -(x) = nxn-1, for any positive integer n. dx -an-38³ +...+ to
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