Problems For Section 5.1

Find the following limits. Your answer should be a real number, ∞, -∞, or "does not exist."

69           Prove that if lim_x→c f(x) = ∞ then lim_x→c 1/f(x) = 0.

71            Prove that if lim_x→c f(x) = 0 and f(x) > 0 for all x, then lim_x→c 1/f(x) = ∞.

72            Prove that if lim_x→c f(x) exists or is infinite, then

lim_x→0+ f(x) = lim_t→∞ f(1/t).

73            Prove that if lim_x→∞ f(x) exists or is infinite then

lim_x→∞ f(x)= lim_t→0+ f(1/t).