I need help on some past paper exam questions with some working out... not really sure how to attempt these ones in particular

1. 

Which of the following is equal to the limit lim In(sin(a) + 20), if it exists? I+ +00 (a) Does not exist (b) 3 ( C) TT (d) tooConsider the function f : R - R defined by the following rule: 7, if x = 3, f(x) = x2 + x - 12 if x # 3. x - 3 How many horizontal asymptotes does f have? (a) 2 (b) 0 (c) 1 (d) 3Suppose 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 manyWhich of the following is equal to the limit lim M, if it exists? Ib'u' 31: (a) 1 (b) l (c) 0 (d) Does not exist Suppose that f : R > R is a function such that lim f (.13) does not exist. Which of the following :42 statements must be true, for any such function f ? (a) f is not a continuous function at a: = 2. (b) At least one of the two limits 11111 f (cc) , lim at) must not exist. ) ) :nr2' 342+ (c At least one of the two limits lim f (cc) , lim f(:c) must be innite. :ct2' 342+ (d f(2) does not exist