MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) 6 B) 14 C) 10 D) Does not exist

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1 Assn Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the limit, if it exists. 1) Find: lim x -1 6x + 5 5x - 6 A) -11 B) C) 1 11 D) 1 1) Solve the problem. 2) The cost of manufacturing a particular videotape is C(x) = x, where x is the number of tapes produced. The average cost per tape, denoted by C(x), is found by dividing C(x) by x. Find lim x 9000 C(x). A) 6 B) 14 C) 10 D) Does not exist 2) Use the graph to evaluate the indicated limit and function value or state that it does not exist. 3) Find lim x 0 f(x) and f(0). 3) A) 6; 0 B) 0; 6 C) Does not exist; 6 D) 0; does not exist Sketch a possible graph of a function that satisfies the given conditions. 1

2 4) f(0) = 6; lim f(x) = 0; x 0- lim f(x) = 0 4) x 0+ A) B) C) D) Find the limit, if it exists. 5) Find: lim x - 4 x2-16 x + 4 A) 8 B) -8 C) 16 D) ) 2

3 6) Find: lim x 5 x - 5 x - 5 A) -1 B) 1 C) 0 D) Does not exist 6) 7) Given lim f(x) = -2 and lim x 4 x 4 g(x) = 5, find lim x 4 [g(x) - f(x)]. 7) - 4 f(x) A) 7 8 B) C) D) 3 8 8) Evaluate the following limit. 1 lim x 2 x - 2 A) - B) 2 C) D) Does not exist 8) Sketch a possible graph of a function that satisfies the given conditions. 9) f(1) = 4; lim f(x) = 4; x 1- x 1+ lim f(x) = 3 9) A) B) 3

4 C) D) Find the limit, if it exists. 10) Find: lim h 0 f(7 + h) - f(7) h for f(x) = -x ) A) 1 B) 0 C) -1 D) Does not exist Use or where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes. 11) g(x) = x 11) 6 - x A) lim f(x) = ; x 6- lim B) lim f(x) = ; x 6- lim C) lim f(x) = ; x 6- lim D) lim f(x) = ; x 6- lim f(x) = ; x = 6 is a vertical asymptote x 6+ f(x) = ; x = 0 is a vertical asymptote x 6+ f(x) = ; x = 6 is a vertical asymptote x 6+ f(x) = ; x = 6 is a vertical asymptote x 6+ Use the given graph to find the indicated limit. 12) 12) lim f(x) x 2+ A) B) 2 C) 0 D) 4

5 13) 13) Find lim f(x). x A) B) 4 C) D) 3 Provide an appropriate response. 14) If the limit at infinity exists, find the limit. lim x 3x3 + 5x 4x4 + 10x ) A) B) 1 C) 3 4 D) 0 Solve the problem. 15) Suppose that the value V of a certain product decreases, or depreciates, with time t, in months, where 16t2 V(t) = 23 - (t + 2) 2. Find lim V(t). t A) 23 B) 16 C) 7 D) 19 15) Provide an appropriate response. 16) Find the horizontal asymptote, if any, of the given function. (x - 3)(x + 4) f(x) = x2-4 A) x = 2, x = -2 B) y = 1 C) y = 3, y = -4 D) None 17) Find the horizontal asymptote, if any, of the given function. f(x) = 2x 3-3x - 9 9x3-5x ) 17) A) y = 3 5 B) y = 2 9 C) y = 0 D) None 5

6 Use the given graph to find the indicated limit. 18) 18) Find lim f(x). x A) 4 B) 3 C) D) 19) 19) lim f(x) x 4- A) B) 4 C) 0 D) Find the limit. 20) Determine the limit. x2 lim f(x), where f(x) = x 5+ (x - 5)3 A) B) 5 C) -2 D) - 20) Sketch a possible graph of a function that satisfies the given conditions. 6

7 21) f(0) = 6 and lim f(x) = 6 21) x 0 A) B) C) D) 7

8 22) f(-1) = -7 ; lim f(x) = -2; x (-1)- lim f(x) = -7 22) x (-1)+ A) B) C) D) 8

9 Solve the problem. 23) The cost of renting a snowblower is $20 for the first hour (or any fraction thereof) and $5 for each additional hour (or fraction thereof) up to a maximum rental time of 5 hours. Write a piecewise definition of the cost C(x) of renting a snowblower for x hours. Is C(x) continuous at x = 2.5? 25 if 0 < x 1 20 if 0 < x 1 30 if 1 < x 2 25 if 1 < x 2 A) C(x) = 35 if 2 < x 3 40 if 3 < x 4 45 if 4 < x 5 ; No B) C(x) = 30 if 2 < x 3 35 if 3 < x 4 40 if 4 < x 5 ; Yes 23) C) C(x) = 20 if 0 < x 1 25 if 1 < x 2 30 if 2 < x 3 ; No D) C(x) = 35 if 3 < x 4 40 if 4 < x 5 20 if 0 x 1 25 if 1 x 2 30 if 2 x 3 ; No 35 if 3 x 4 40 if 4 x 5 Provide an appropriate response. 24) Use a graphing utility to find the discontinuities of the given rational function. x2 + 2x + 1 f(x) = x3 + 2x2 + 5x - 8 A) 3 B) 1 C) -1 D) Continuous at all values of x 25) Use a sign chart to solve the inequality. Express answers in interval notation x - 4 > 0 24) 25) A) -, B) -, 4 3 C) - 4, D) (0, ) 3 26) Use a sign chart to solve the inequality. Express answers in interval notation. x2 + 6 < 2x A) B) (-, -2) C) {2} D) (2, ) 26) 27) Determine where the function H(x) = x is continuous. 27) x2 + x - 6 A) (-3, 2) (2, ) B) (-, -3) C) (-, -3) (-3, 2) (2, ) D) (-, -3) (-3, 2) 28) Solve the inequality and express the answer in interval notation: x2-4x x + 5 > 0. 28) A) (-5, 0) B) (-5, ) C) (4, ) D) (-5, 0) (4, ) 29) Determine the points at which the function is discontinuous. h(x) = x2-9 for x < -1 0 for -1 x 1 x2 + 9 for x > 1 A) -1, 1 B) 1 C) -1, 0, 1 D) None 29) 9

10 30) Determine where the function f(x) = 5x is continuous. 30) 2x - 3 A) (-, ) B) -, , C) -, 3 2 D) 3 2, 10