Practice Problem Set, L10-12

Practice Problem Set, L10-12 - Calculus I- Practice Problem...

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Calculus I- Practice Problem Set, Lectures 10 - 12, Spring 2011 1. Evaluate the limits: a) lim x !¡1 1 ¡ 2 x p x 2 + 1 b) lim x !¡1 5 x ¡ 1 j 3 x + 2 j 2. Which of the following functions has a horizontal asymptote of y = ¡ 1 2 and only one vertical asymptote of x = ¡ 2? Circle the correct answer. a) f ( x ) = 1 + 2 x 3 16 ¡ 4 x 3 b) f ( x ) = x 2 8 ¡ 2 x 2 c) f ( x ) = 2 x ¡ x 2 2 x 2 ¡ 8 d) f ( x ) = 2 + x 2 4 ¡ x 2 3. Find: a) lim x !1 p x 2 + x ¡ x b) lim x !¡1 p x 2 + x ¡ x 4. Find all asymptotes of the graph of f ( x ) = 1 1 ¡ 3 e 2 x 5. Find all vertical and horizontal asymptotes of f ( x ) = 2 e x 4 ¡ 3 e x 6. Use the Squeeze Theorem to evaluate: (a) lim x !1 e ¡ x sin x (b) lim x !1 f ( x ) if 6 3 + e ¡ x f ( x ) 2 x 1 + p x 2 ¡ 1 7. Evaluate: (a) lim x !1 tan ¡ 1 1 ¡ x 1 + x · (b) lim x ! ( 2 ) + e tan x (c) lim x ! ( 2 ) ¡ e tan x 8. Use the deflnition of derivative to flnd f 0 ( x ) if f ( x ) = p 2 x ¡ 3 9. The line tangent to the graph of a function f at (3 ; 5) intersects the graph of f at ( ¡ 1 ; ¡ 4).
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This note was uploaded on 05/17/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

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Practice Problem Set, L10-12 - Calculus I- Practice Problem...

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