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 x x 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 x x Æ = ¢ Æ Æ = - ( ) - Æ - ( ) = Æ Ê Ë Á ˆ ¯ ˜ = - - ( ) [ ] = + ( ) Æ + ( ) Æ = 2 2 1 2 2 0 2 4 2 2 2 0 0 0 0 1 2 2 1 2 2 1 2 2 4 1 4 p p p p p p p p 67 4 8 4 } 678 L H b) lim x x x Æ - - 0 2 1 3 1 (4 points) lim lim ln ln ln ln ln ln x x x x x x Æ = = ¢ Æ = = - - Æ - = Æ - = Ê Ë Á ˆ ¯ ˜ = Æ Æ = 0 0 1 0 1 0 0 1 0 1 2 1 3 1 2 1 0 3 1 0 0 0 2 2 3 3 2 2 3 3 2 3 } { } } { L H c) lim ln x x e x Æ + ( ) 3 2 1 (2 points) lim ln ln ln ln x x e x e e e Æ ( ) + ( ) Æ = Æ + ( ) = = 3 2 2 3 6 6 1 3 1 4 4

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d) lim ln x x x x Æ • + 2 1 (10 points) lim ln lim ln lim ln lim / lim x x x x x x x x x x x x x D x x x x Æ • ¢ Æ • Æ • ¢ Æ • Æ • + Æ • Æ • Ê Ë Á ˆ ¯ ˜ = ( )( ) + ( ) Ê Ë Á ˆ ¯ ˜ ¨ = + Æ • Æ • Ê Ë Á ˆ ¯ ˜ = = = • 2 1 2 1 1 2 1 2 1 2 L H L H By Product Rule for } } e) lim cot x x x Æ + 0 (8 points) lim cot lim tan tan lim sec lim cos cos x x 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 0 0 0 0
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