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(CY EXERCISES 1. Complete the following table. lim 2016 T-+C lim r -2 -1/2 0 3.1416 10 V3 /2. Assume the following: lim f(x) = - I -+ lim g(r) = 12, and lim h(r) = -3. rtc Compute the following limits: a. lim (-4 . f(I)) g. lim (4 . f(x) + h(x)) b. lim V 12 . f(x) h. lim (8 . f(x) - g(x) - 2 . h(x)) c. lim (g(x) - h(I)) d. lim (f (x) . 9(I)) I )C i. lim (f(x) . g(z) . h(I)) j. lim v-g(x) . h(x) e. lim 9(r) + h(x) r-+c r-+c k. lim g(I) I-c (h(x) )2 f. lim I-+c 1. lim 9(I) I re (h(x) )2 J(I) 3. Determine whether the statement is True or False. If it is false, explain what makes it false, or provide a counterexample. a. If lim f(x) and lim g(x) both exist, then lim (f(x) + g(x)) always exists. I-+C b. If lim f(r) and lim g(r) both exist, then lim (f(x) . g(x)) always exists. c. If lim f(x) and lim g(r) both exist, then lim () r-c g(I) always exists. d. If lim f(x) exists and p is an integer, then lim (f(x)), where p is an integer, always exists. e. If lim f(r) exists and n is a natural number, then lim Vf(r), always exists. J. Assume the following I-+C' lim f(x) = 1, lim g(x) = -1, and lim h(x) = 2. Compute the following limits: a. lim (f (x) + 9(x)) I-+ C i. lim (f(z) . g(x) . (h(x))2) b. lim (f(x) - g(x) - h(x)) I C" j. lim 1 c. lim (3 . g(x) + 5 . h(x)) rc f(x) d. lim vf(x) k. lim I-+c reg(x) e. lim vg(I) 1. lim rach(I) f. lim Vg(x) I +C m. lim g. lim (h(x))5 I-cf(x) - h(I) h. lim g(x) - f(I) n. lim h(x) I-+C f (I) + 9(I) 5. Assume f(r) = r. Evaluate a. lim f(x) f. lim ((f(x))2 - f(x)). g. lim ((f(z))3 + (f(x))2+2 . f(x)). b. lim AS(I) h. lim V/3 (f(x) )2 +4 - S(x). C. I-4 (f(x) )2 (f (x) ) 2 - f(x) i. lim d. lim -Vf(x). x -+ 4 5. f(x) 1-+4 (f(x) )2 - Af(1) e. lim V9 . f(I) j. lim I- (f (I) ) 2 + 4f(I)