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SCHUMITZ3HW - Math 118 Homework 1 Solutions 1. (15)...

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Math 118 Homework 1 Solutions 1. (15) Evaluate the following limits. If the limit is infinite, indicate + or - . a) 2 2 1 x 2 3 lim x 2 x x x + - + - = 4/3 2 2 1 x 2 3 ( 1)( 3) ( 3) (1 3) x 2 ( 1)( 2) ( 2) (1 2) x x x x x x x x x = + - - + + + = = = + - - + + + b) 2 0 1 1 ( ) lim x x x x - + = 1 2 2 2 2 2 2 0 1 1 1 = 1 ( ) ( ) ( 1) ( 1) x x x x x x x x x x x x x x x xx x x = + - - = = = = + + + + + c) 2 lim ( 4 -2 ) x x x x → ∞ + = 1/4 2 2 2 2 2 2 2 ( 4 +2 ) 4 4 ( 4 -2 ) ( 4 +2 ) ( 4 +2 ) ( (4 1/ ) +2 ) 1 1 1/ 4 ( 4 1/ +2 ( 4 1/ +2 ( 4 +2 x x x x x x x x x x x x x x x x x x x x x x x x x =∞ + + - + = = + + + = = = = + + 2. (5) For what value(s) of c is the function ( ) f x continuous at 1 x = ? 2 ( ) , if 1 1, if 1 f x x c x c x x = + < = + 1 2 1 2 2 2 lim ( ) 1 lim ( ) 1 Set equal: 1 1 0 ( 1) 0 0 or 1 x x f x c f x c c c c c c c c c c c - + = + = + + = + → = - = - = → = = 3. (20) Assume the curve 2 3 2 ( 2 ) 2 64 x y xy + = + defines as a function of y x . a) Calculate
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SCHUMITZ3HW - Math 118 Homework 1 Solutions 1. (15)...

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