# horizontal asymptotes

2+00 1. Which of the following is equal to the limit limIn(sin(2) +20), if it exists? (a) Does not exist (b) 3 (c) (d) to 2. Consider the function f : RR defined by the following rule: 7, if x = 3, f(3) = c? + – 12 if : 73 2-3 How many horizontal asymptotes does f have? (a) 2 (b) 0 (c) 1 (d) 3 3. Suppose that f:R + R is continuous on all of R. What is the maximum number of distinct vertical asymptotes that f can have? (a) 0 (b) 1 (c) 2 (d) Infinitely many 4. Which of the following is equal to the limit lim cos()(x – 1) if it exists? (a) -1 (b) 1 (c) o (d) Does not exist 2 – 7 5. Suppose that f: R+R is a function such that lim f(t) does not exist. Which of the following statements must be true, for any such function f ? (a) f is not a continuous function at x = 2. (b) At least one of the two limits lim f(x), lim f(x) must not exist. (c) At least one of the two limits lim f(), lim f(x) must be infinite. (d) f(2) does not exist. 2-2- 2+2+ 2+2 2+2+

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