Math151OldSols2

Math151OldSols2 - QUIZ ON CHAPTER 10 SOLUTIONS MATH 151...

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QUIZ ON CHAPTER 10 SOLUTIONS MATH 151 – SPRING 2003 – KUNIYUKI 100 POINTS TOTAL 1) Find the limits. Write or -• when appropriate. If a limit does not exist, and and are inappropriate, write “DNE” (Does Not Exist). Indicate indeterminate forms whenever appropriate, though you don’t have to indicate signs for them. (46 points total) a) lim cos x xx x Æ - - () 2 2 2 4 p (6 points) lim cos cos lim sin lim sin sin x x x x x x x x Æ = ¢ Æ Æ = - - Æ- = Æ Ê Ë Á ˆ ¯ ˜ = -- [] = + () Æ+ () Æ = 2 2 1 2 2 0 2 4 22 2 0 0 0 0 12 2 2 2 4 1 4 pp 67 48 4 } 678 LH b) lim x x x Æ - - 0 21 31 (4 points) lim lim ln ln ln ln ln ln x x x x x x Æ = = ¢ Æ = = - - = = Ê Ë Á ˆ ¯ ˜ = Æ Æ = 0 0 1 0 1 0 0 1 0 1 0 310 0 0 22 33 2 3 } { } } { c) lim ln x x e x Æ + 3 2 1 (2 points) lim ln ln ln ln x x e x ee e Æ + Æ= Æ+ = = 3 3 6 6 13 1 4 4
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d) lim ln x x xx Æ• + 2 1 (10 points) lim ln lim ln lim ln lim / lim x x x x x x x x x D x x x x ¢ ¢ Ê Ë Á ˆ ¯ ˜ = ()( ) + () Ê Ë Á ˆ ¯ ˜ ¨ = + Ê Ë Á ˆ ¯ ˜ = = =• 2 1 2 1 1 2 1 2 1 2 LH By Product Rule for } } e) lim cot x Æ + 0 (8 points) lim cot lim tan tan lim sec lim cos cos x x x x x x x x Æ Æ ¢ Æ Æ + + + + ◊• = Æ Æ= Ê Ë Á ˆ ¯ ˜ = = = =() = 0 0 0 2 0 2 2 2 0 0 00 0 0 1 0 1 1 } f) lim cos / x x x Æ 0 1 2 (16 points) lim cos / x x x Æ 0 1 2 1 Let Note: > 0 near = yx x x y x x x x x x x
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Math151OldSols2 - QUIZ ON CHAPTER 10 SOLUTIONS MATH 151...

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