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Unformatted text preview: Exercises UF Calculus Set 8 1. Let f , g , h , k be nonnegative functions with limits , 1 , 1 , , respectively, as x a . What are the limits of the functions below as x a ? If it cannot be determined, write unknown. (a) 4 f 2 g (b) h k (c) f g h (d) h g + k (e) h ( f + g ) (f) h k f 2. Carefully justify the limits, step by step, from the limit laws. (a) lim x 2 x 2 1 x 3 = 3 (b) lim x 1 p x 2 + 3 x = 2 3. In each case, find a simple transformation of g ( x ) that is identical to f ( x ) for all points except those indicated. Use this fact to sketch the function f ( x ) . (a) f ( x ) = 2 x 2 + 5 x + 2 x 2 + 2 x ; g ( x ) = 1 x ; x = 2 (b) f ( x ) = x 1 x 1 1 x ; g ( x ) = x ; x = 0 , 1 (c) f ( x ) = ln x x 2 + x ; g ( x ) = ln x ; x = 0 4. Evaluate the limits: (a) lim x x + 1 1 x (b) lim x ( a + x ) 2 a 2 x (c) lim x 3 ( x 2 9) 2 ( x 3) 2 (d) lim x  x p 1 + x 2 (e) lim x 2 x 2 + 1 x 3 x 2 4 (f) lim x...
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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.
 Spring '08
 ALL
 Calculus, Geometry, Limits

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