1. For each of the following, find the limit if it exists. [points 10] 2 (a). lim J x-+00 Vx- 1 (b). lim (x - x -4) X-+00 (c). lim 10 -x X-+00 (d). lim 2x* + 4x2+ 2 *+00 *'5 - 10x3 + 2x2 + 2 2. For each of the following, find the limit if it exists. [points 12] (a). lim (Vx -2 + 1) x-2+ (b). lim x-3+ X - 3 (c). lim 1 x-0+ 3. For each of the following, find the limit if it exists. [points 12] (a). lim cost x-0- (b). lim (10 + x + 5*) x-0+ (c). lim (10 + x + 5*) x-0 - 4. For each of the following, find the limit, if it exists. (m is a positive integer) [points 10] (a). lim (2x3 + 4x2 + 2) x-3(b). lim (2x2 - 4x + 2)' x-2 1+x-x3 (c). lim- x-2 1+x2 (d). lim * - 2x + 1 * - x x" - 1 (e). lim x-1 x-1 5. For each of the following, find the limit if it exists. [points 10] x - 1 (f). lim x-1x-1 (g). lim Vi+x-1 1+0 (h). lim Vi+ x-Vi+x x2 - 1 (i). lim 2 x-1*+x-2 x - 1 (j). lim 2 x-1*-x+2 6.Calaulate [points 6] 1 - cosx lim 7. The concentration C of a drug in a patient's bloodstream t hours after it was injected is given by [points 5] 0.2+2 C(t) = - +3 + 3+2 + 20 (a) Find lim C(t). t-+00(b) Interpret the result in (a). 8. Let P be a polynomial, we have lim P(x) - x3 - = 2, and lim x P() - 1, find P(x). [points 5] X-+00 x-0