a151q2wi - x -2 f ( x ) Answer : 1 (iv) Find lim x -f ( x )...

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MATH 151 Answers to Assignment 2 Autumn 2009 1. Find lim x →-∞ x 4 1+ x 4 . x 4 1+ x 4 = x 4 ± x 4 ( 1 x 4 + 1) = x | x | 4 ± 1 x 4 +1 x →-∞ -----→ - 1 1 4 0+1 Answer : - 1 2. Find the asymptotes to the graph of y = 9 - x 2 x 2 - 5 x +6 . (3 - x )(3 + x ) ( x - 3)( x - 2) = - x +3 x - 2 . Answer : x = 2 and y = - 1 3. Find lim x 0 csc(5 x ) cot(3 x ) . 1 sin(5 x ) cos(3 x ) sin(3 x ) = sin(3 x ) cos(3 x ) sin(5 x ) = (3 x ) sin(3 x ) 3 x cos(3 x ) (5 x ) sin(5 x ) 5 x = 3 sin(3 x ) 3 x cos(3 x )5 sin(5 x ) 5 x ---→ x 0 3 · 1 1 · 5 · 1 Answer : 3 5 (over) Typeset using A M S -T E X.
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MATH 151 Answers to Assignment 2, p .2 Autumn 2009 4. Find the following limits, where f ( x )= 2 x/ ( x - 2) if x< - 2 - x/ 2 if - 2 <x 0 e - x if 0 <x . (i) Find lim x →- 2 - f ( x ) lim x →- 2 - f ( x ) = lim x →- 2 - 2 x x - 2 = 2( - 2) - 2 - 2 . Answer : 1 (ii) Find lim x →- 2 + f ( x ) lim x →- 2 + f ( x ) = lim x →- 2 + - x 2 = - - 2 2 . Answer : 1 (iii) Find lim
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Unformatted text preview: x -2 f ( x ) Answer : 1 (iv) Find lim x -f ( x ) lim x -f ( x ) = lim x -x 2 = 2 . Answer : (v) Find lim x + f ( x ) lim x + f ( x ) = lim x + e-x = e-. Answer : 1 (vi) Find lim x f ( x ) Answer : Does not exist (vii) Find lim x f ( x ) lim x f ( x ) = lim x e-x . Answer : (viii) Find lim x - f ( x ) lim x - f ( x ) = lim x - 2 x x-2 . Answer : 2 end...
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a151q2wi - x -2 f ( x ) Answer : 1 (iv) Find lim x -f ( x )...

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