MTH132-Quiz5-Solutions

MTH132-Quiz5-Solutions - Page 1 Name(Print Clearly Student...

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Unformatted text preview: Page 1 10/18/2011 Name (Print Clearly): Student Number: MTH132 Section 5 & 18, Quiz 5 1 [3 pts each] . Find the limits. (a) 4 / cos sin lim 4 / π π-- → x x x x ( it is 0/0, so we can use L’H) 2 2 2 2 2 1 sin cos lim 4 / = + = + = → x x x π (b) ) 1 1 ( lim x x x- + → (it is ∞- ∞ , so we need to convert it to 0/0 first) ) ( lim x x x x x- = + → ( it is 0/0, so we can use L’H) ∞ =- =- → + ) 2 / 3 1 2 / 1 ( lim 2 / 1 2 / 1 x x x ) 1 ( ∞ =- ∞ + or ∞ =- =- + + → → ) 1 ( lim ) ( lim x x x x x x x x (divide by x , and ) 1 ∞ =- + (c) ) ( lim 2 x x x x +- ∞ → ) / 1 1 1 ( 1 lim ) ( lim ) ( ) )( ( lim 2 2 2 2 x x x x x x x x x x x x x x x x x + +- = + +- = + + + + +- ∞ → ∞ → ∞ → (divide by x ) = 2 1 1 1 1- = + +- 2. Suppose 4 3 4 ) ( x x x f- = . (a) [2 pts]. Find ) ( ' x f and ) ( ' ' x f . Page 2 10/18/2011 3 2 4 12 ) ( ' x x x f- = and 2 12 24 ) ( ' ' x x x f- = (b) [4 pts]. Find all critical points and inflection points. Use first derivative test to find local extreme values.(b) [4 pts]....
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MTH132-Quiz5-Solutions - Page 1 Name(Print Clearly Student...

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