UFCalcSet26

# UFCalcSet26 - Exercises UF Calculus Set 26 1 Let f g h be...

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Exercises UF Calculus Set 26 1. Let f , g , h be nonnegative functions with limits 0 , 1 , , respectively, as x a . What are the limits of the functions below as x a ? If it cannot be determined, write ”indeterminate” and the indeterminate form. (a) ( g ( x ) + f ( x )) h ( x ) (b) f ( x ) h ( x ) (c) (1 + g ( x )) - h ( x ) (d) h ( x ) f ( x ) g ( x ) (e) (1 - g ( x )) f ( x ) (f) h ( x ) 1 f ( x ) 2. Evaluate the limits; ﬁrst show that it is of the form ( 0 0 ): (a) lim x 2 2 - x + 2 4 - x 2 (b) lim t 1 + 1 t - 1 t 2 - 2 t + 1 (c) lim t 0 t 2 e t - t - 1 (d) lim x 0 x + 1 - 1 x + 4 - 2 (e) lim x 1 x - 1 3 x - 1 (f) lim t →- 1 + 3 t + 1 t + 1 (g) lim x 1 x ln( x ) x 2 - 1 (h) lim x 0 sin(2 x ) ln( x + 1) (i) lim x 0 x + e x - e 2 x 1 - cos(2 x ) 3. For each limit, either evaluate immediately, or if it is indeterminate, write the form it repre- sents, and then evaluate using the methods of this section. (a)

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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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UFCalcSet26 - Exercises UF Calculus Set 26 1 Let f g h be...

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