homework1 - M408C Homework 8/30 9/27 8/30 Plot the slopes...

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Unformatted text preview: M408C Homework: 8/30 - 9/27 8/30 Plot the slopes of the tangent lines of y = x 3 . 9/4 Give the definitions of the derivatives of f ( x ) = e x and g ( x ) = x √ x/ tan x . If f ( x ) = x 3 , plot the slopes of the tangent lines. Then use the definition to show that f ( x ) = 3 x 2 . Find the tangent line at x =- 2. Repeat this for f ( x ) = 1 /x, x = 2. Let f ( x ) = x 2- 3 x + 1. Use Newton’s Method to find x 3 , given that x = 0. If you want to use Newton’s Method to approximate 3 √ 17, what should f ( x ) be? From the textbook, p.131 #3, 10. 9/6 If f ( x ) = x 3 + x- 3 and x = 1, use Newton’s Method to find x 1 , x 2 , x 3 . Differentiate the following. Do the second one in two different ways. (a) 3 x 3 + 4 x 2 + 2 x + 3 1 x + √ x , (b) (3 x + 2)( x 2 + 2 x + 1) 9/11 Differentiate the following. (a) x 3 + 3 √ x 2 x 3- 3 x 2 , (b) 7 x 2 5 x 3 + 2 x 2 + 2 x + 3 9/13 Calculate d dx cos x in the following ways: (a) directly from the definition, using the identity for cos(...
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This homework help was uploaded on 04/09/2008 for the course M 408c taught by Professor Mcadam during the Fall '06 term at University of Texas.

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