classwork4 - Classwork IV Sections 2.8, 2.9 x2 = x 5 - x3 t...

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Classwork IV Sections 2.8, 2.9 lim x →∞ x 2 5 - x 3 = (This is 2.8.2). lim t →-∞ t t - 5 = (2.8.4). lim x →∞ ± 2 x 2 + 3 - 2 x 2 - 5 ² = (2.8.17). lim t →- 1 - 2 t 2 - t - 2 - 3 t + 1 = lim t →- 1 + 2 t 2 - t - 2 - 3 t + 1 = lim t →- 1 2 t 2 - t - 2 - 3 t + 1 = Find the horizontal and vertical asymptotes for the graph of f ( x ) = 3 x + 1 and sketch its graph. (2.8.37). Let f ( x ) = 1 x - 1 . Then f ( - 2) = - 1 3 and f (2) = 1. Is there a number c , - 2 c 2 such that f ( c ) = 0? Explain. (2.9.46). Let f ( x + y ) = f ( x ) + f ( y ) for all x and y in R and suppose that f is continuous at x = 0. Prove that f is continuous everywhere. (2.9.49a). Find k such that f ( x ) = ³ kx + 1 if x 2 kx 2 if x > 2 is continuous. Where is g ( x ) = x if x 1 x 2 if 1 < x 2 sin x if x > 2 continuous? Suppose g ( x ) = | f ( x ) | is continuous. Is it necessarily true that f ( x ) is continuous? Prove it or give a counterexample. (2.9.55).
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