Then x b x c x c 2 57 y sec

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Unformatted text preview: t; lx l € B so that lim x Ä ! lx l c2 (x c 3) # 47. For every real number cB  0, we must find a $ € 0 such that for all x, 0  kx c 0k  $ Ê c" x  cB. Now, " ÈB œ _.  cB. € B. Section 2.5 Infinite Limits and Vertical Asymptotes (c) We say that f(x) approaches minus infinity as x approaches x! from the left, and write lim f(x) œ c_, if for every positive number B (or negative number cB) there exists a corresponding number $ € 0 such that for all x, x! c $  x  x! Ê f(x)  cB. 52. For B € 0, 53. For B € 0, " x " " € B € 0 Í x  B . Choose $ œ B . Then !  x  $ Ê 0  x  " B 97 54. For B € !, 55. For B € 0, Ê " xc# " xc# " " € B Í !  x c 2  B . Choose $ œ B . Then #  x  # b $ Ê !  x c #  $ Ê !  x c 2  $ Ê # 57. y œ sec x b " x 58. y œ sec x c # c # " #B . " 1cx Then " c $  x  " Ê c$  x c 1  0 Ê " c x  $  € B for !  x  1 and x near 1 Ê xÄ" # 56. For B € 0 and !  x  1, " 1cx b € B € ! so tha...
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