assignemtn2 - MAT 1339C Assignment 2 (Due MON. NOV. 1st,...

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Unformatted text preview: MAT 1339C Assignment 2 (Due MON. NOV. 1st, 5:30) Student Number : Name: Problem 1: Find the equation of the tangent line to the graph of f ( x ) = x 2 sin(2 x ) at x = . Work: Compute f ( x ) = 2 x sin(2 x ) + x 2 cos(2 x )2 by product rule (and chain rule). Plug in and get f ( ) = 0 + 2 2 = 2 2 . Let y = mx + n be the equation of the tangent line. Then m = f ( ) = 2 2 . Thus y = 2 2 x + n . Note that f ( ) = 0, hence 0 = 2 2 + n . Hence n =- 2 3 . We got y = 2 2 x- 2 3 Problem 2: Using the rules of differentiation find the derivative of g ( x ) = cos(2 x )+ x- 2 sin(2 x ) . Work: By quotient rule and chain rule one has that g ( x ) = {- sin(2 x )2+1 } sin(2 x )-{ cos(2 x )+ x- 2 } cos(2 x )2 sin 2 (2 x ) . No need for simplifications! Problem 3: If g ( x ) = 5sin(4cos(3 x )) find the derivative of g ( x ). Work: Using 2 times chain rule one gets: g ( x ) = 5cos(4cos(3 x ))4(- sin(3 x ))3 =- 60cos(4cos(3 x ))sin(3 x )....
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This note was uploaded on 09/20/2011 for the course SCIENCE MAT1330 taught by Professor Rad during the Spring '11 term at University of Ottawa.

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assignemtn2 - MAT 1339C Assignment 2 (Due MON. NOV. 1st,...

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