m21am1sol - MAT 21A SECTION D: CALCULUS FIRST...

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Unformatted text preview: MAT 21A SECTION D: CALCULUS FIRST MIDTERMSOLUTIONS DATE AND TIME: FRIDAY, OCTOBER 20, 2006. 2:103:00. ROOM: 100 HUNT HALL INSTRUCTOR: M. MULASE Problem 1 (10 points) . This problem concerns various limits. Give your answer in its simplest form in the space provided. lim x 1 x x = 1; lim x + x x = lim x + 1 x = + ; lim x + x x = lim x + 1 x = 0 lim x 1 1- x 1- x = lim x 1 1 1 + x = 1 2 lim x + 1- x 1- x = lim x + 1- 1- = 1 lim x 1 x 2- 2 x + 1 x 2- 1 = lim x 1 x- 1 x + 1 = 0 lim x - x 2- 2 x + 1 x 2- 1 = lim x - x- 1 x + 1 = lim x - x x + 1 + lim x -- 1 x + 1 = 1 lim x 1 x- 1 x 2- 1 = lim x 1 1 x + 1 = 1 2 lim x 1- x + 1 x 2- 1 = lim x 1- 1 x- 1 =- lim h ( x + h ) 3- x 3 h = lim h x 3 + 3 hx 2 + 3 h 2 x + h 3- x 3 h = lim h (3 x 2 + 3 hx 2 + h 2 ) = 3 x 2 1 2 TOTAL POINTS FROM THIS PAGE = Problem 2 (10 points) . Let us consider the function f ( x ) = sin x x...
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This note was uploaded on 10/07/2008 for the course MATH 21A taught by Professor Osserman during the Spring '07 term at UC Davis.

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m21am1sol - MAT 21A SECTION D: CALCULUS FIRST...

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