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Unformatted text preview: explain your answer. 2. Is there a real number a such that the following function is continuous on R ? f ( x ) = ± 3 √ x if x ≥ a, 1x if x < a. 3. Evaluate the following limits if they exist. (a) lim x →∞ arctan( xx 4 ) (b) lim x →∞ √ 9 x 6x x 3 + 1 (Hint: Compare with Exercise #23 in Section 2.6.) 1 (c) lim x →∞ ( x + √ x 2 + 2 x ) (Hint: Compare with Exercise #25 in Section 2.6.) 4. Determine whether f (0) exists when f ( x ) = ( x 2 sin 1 x if x 6 = 0 , if x = 0 . 5. Suppose f is a function with the property that  f ( x )  ≤ x 2 for every real number x . (a) Show that f (0) = 0 . (b) Show that f (0) = 0 . 2...
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This note was uploaded on 12/18/2010 for the course ECONOMICS 120 taught by Professor Mesta during the Spring '10 term at Wilfred Laurier University .
 Spring '10
 Mesta

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