275_infinite_limits

# 2 g x f x 0 4 give examples of functions f x g x for

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2 - g ( x ) /f ( x ) = 0. 4. Give examples of functions f ( x ), g ( x ) for which we have lim x 0 f ( x ) = , lim x 0 g ( x ) = and (a) lim x 0 f ( x ) - g ( x ) = 5 (b) lim x 0 f ( x ) - g ( x ) = (c) lim x 0 f ( x ) - g ( x ) = -∞ (d) lim x 0 f ( x ) - g ( x ) does not exists. 5. Show that for any non-constant polynomial p ( x ) the limit of p ( x ) will be or -∞ ad x → ∞ or x → -∞ . 6. Show that a rational function will have a finite nonzero limit at infinity if the degrees of the denominator and numerator are the same, and it will have a limit equal to zero if the degree of the numerator is smaller than the degree of the denominator. 7. Find the following limits (you may use the limit laws) (a) lim x 1 - x x 3 - 1 (b) lim x 3 + x 2 - 2 x 3 - x (c) lim x →-∞ x 2 x 3 +3 x - 2 (d) lim x →∞ x 2 - 3 x x 4 +5 x - 2 (e) lim x →∞ x - 2 - x - 4 Hint: You cannot use the limit laws immediately! 3
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