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Unformatted text preview: x → cos(3 x ) sin(5 x ) cos(2 x ) sin(6 x ) [3] (c) lim x → + ∞ 6 x + 1 √ x 21 + x [3] 4 4. Let f ( x ) = 3 x 2 + 1 x1 . (a) Find all horizontal, vertical, and oblique asymptotes of f . [6] (b) Guess the graph of f and draw a rough sketch. [2] (c) Does f have an inverse? State ( brieﬂy ) a reason for your answer. [2] 5 5. Let f ( x ) = 4 e 1 /x + 6 6 e 1 /x + 9 . (a) Find lim x →e 1 /x . [2] (b) Find lim x → + e 1 /x . [2] (c) Which of the following statements is true? Justify your answer. [6] (i) f has a vertical asymptote at x = 0 . (ii) f has a jump discontinuity at x = 0 . (iii) f has a continuous extension to x = 0 . 6...
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 Fall '10
 b
 Topology, lim cos, MAT 134Y5Y Term, lim e1/x

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