MULTIPLE CHOICE Choose the one alternative that best completes the statement or answers the question Decide whether the limit exists If it exists, find its value 1) 1) _ Find f(x) and A) -5; -2 f(x) B) -7; -5 C) -7; -2 D) -2; -7 2) 2) _ Find f(x) and A) 3; -1 f(x) B) 3; C) - 3; -1 D) -1; 3) 3) _ Find f(x) A) Does not exist B) C) D) 4) 4) _ Find f(x) A) Does not exist B) C) -1 D) 5) 5) _ Find f(x) A) -1 B) C) -2 D) Does not exist 6) 6) _ Find f(x) B) -2 A) C) Does not exist D) 7) 7) _ Find f(x) A) B) Does not exist C) D) 8) 8) _ Find f(x) B) -1 A) 9) Find f(x) C) D) Does not exist 9) _ A) Does not exist B) C) -2 D) -1 10) 10) Find A) -1 f(x) B) Does not exist C) Use the graph to determine whether each statement is true or false 11) A) True 11) B) False 12) 12) A) False 13) D) -2 B) True 13) _ _ A) False B) True 14) 14) f(x) = A) True B) False 15) 15) A) True 16) B) False 16) A) True B) False 17) 17) A) True B) False 18) 18) A) True B) False 19) 19) A) True 20) B) False 20) _ _ A) False B) True Graph the function and then find the specified limit When necessary, state that the limit does not exist 21) f(x) = ; f(x) A) B) f(x) = C) f(x) = D) f(x) = 21) f(x) = 22) 22) f(x) = ; A) f(x) B) f(x) = C) f(x) = D) f(x) = f(x) = -5 23) 23) f(x) = ; f(x) A) B) f(x) = C) D) f(x) = 24) f(x) = -4 f(x) does not exist ; f(x) f(x) does not exist 24) _ _ A) B) f(x) = -4 C) f(x) = D) f(x) = 25) f(x) = 25) y = x2 - 5; f(x) A) B) f(x) = -5 f(x) = C) D) f(x) = -5 f(x) = 26) 26) f(x) = ; A) f(x) = f(x) 176) Graph f(x) = - and the tangent line to the graph at the point whose x-coordinate is A) B) C) D) 177) Graph f(x) = -3x + and the tangent line to the graph at the point whose x-coordinate is -3 A) The tangent line is identical to the graph of the original function 176) _ 177) _ B) C) D) The tangent line is identical to the graph of the original function 178) 178) _ Graph f(x) = A) + and the tangent line to the graph at the point whose x-coordinate is B) C) There is no tangent line for x = Th er e is no ta ng en t lin e fo rx = D) Find the derivative of the function and evaluate the derivative at the given x-value 179) f(x) = at x = A) f'(x) = 3x; f'(1) = C) f'(x) = 6x; f'(1) = 180) f(x) = 5x + at x = A) f'(x) = 9; f'(2) = C) f'(x) = 0; f'(2) = 179) _ B) f'(x) = 6x; f'(1) = D) f'(x) = ; f'(1) = 180) _ B) f'(x) = 5; f'(2) = D) f'(x) = 5x; f'(2) = 10 181) f(x) = x2 + 5x at x = A) f'(x) = 2x + 5; f'(4) = 13 C) f'(x) = 4x + 5; f'(4) = 21 181) _ B) f'(x) = x + 5; f'(4) = D) f'(x) = 2x - 5; f'(4) = 182) 182) _ f(x) = A) x- at x = 10 B) f'(x) = ; f'(10) = f'(x) = - C) D) f'(x) = - ; f'(10) = - f'(x) = 183) f(x) = 5x2 + x at x = -4 A) f'(x) = 10x - 1; f'(-4) = -41 C) f'(x) = 10x + 1; f'(-4) = -39 B) f'(x) = x + 10; f'(-4) = D) f'(x) = x - 10; f'(-4) = -14 184) _ B) f'(x) = 2x - 3; f'(4) = D) f'(x) = 4x + 1; f'(4) = 17 185) f(x) = x2 + 11x - 15 at x = A) (x) = 2x + 11; (1) = 13 (x) = 2x - 11; ; f'(10) = 183) _ 184) f(x) = 2x2 + x - at x = A) f'(x) = 4x + 3; f'(4) = 19 C) f'(x) = 4x - 1; f'(4) = 15 C) ; f'(10) = - 185) _ (1) = -9 186) f(x) = 3x2 + 5x - at x = -2 A) f'(x) = 3x + 5; f'(-2) = -1 C) f'(x) = 6x - 5; f'(-2) = -17 B) (x) = 11x; D) (x) = 11x + 15; (1) = 11 (1) = 26 186) _ B) f'(x) = 2x + 5; f'(-2) = D) f'(x) = 6x + 5; f'(-2) = -7 187) f(x) = - x3 at x = A) f'(x) = -3x; f'(1) = -3 187) _ B) f'(x) = 3x2 - 1; f'(1) = D) f'(x) = -3x2; f'(1) = -3 C) f'(x) = - 3x; f'(1) = -2 188) 188) _ f(x) = A) at x = -1 B) f'(x) = ; f'(-1) = C) f'(x) = - ; f'(-1) = - f'(x) = ; f'(-1) = -8 D) f'(x) = 8; f'(-1) = Find an equation for the line tangent to the graph of the given function at the indicated point 189) f(x) = at (2, 1) A) y = - B) y = 1x - C) y = 1x - 189) _ D) y = 1x + 190) 190) _ f(x) = A) at (3, 6.75) B) y= x+ C) y= x- D) y= x- y= x+ 191) 191) _ f(x) = at (- 2, - 4) A) y = 6x + B) y = 8x + C) y = 8x + D) y = 2x + 192) 192) _ f(x) = at (2, 8) A) y = - 4x B) y = - 8x + 24 C) y = - 4x + 16 D) y = - 4x + 193) 193) _ f(x) = A) at (9, 5) B) y=- x + 10 194) f(x) = - at (2, 0) A) y = 4x - 195) f(x) = + at (3, 13) A) y = 6x - 196) f(x) = - x at (-4, 20) A) y = -9x - 16 197) f(x) = A) y = -2 C) y=- x+5 D) y=- x + 15 y=- x 194) _ B) y = 4x - 12 C) y = 2x - D) y = 4x - 16 195) _ B) y = 6x - 14 C) y = 3x - D) y = 6x - 10 196) _ B) y = -9x - 12 C) y = -9x + 12 D) y = -9x + 16 197) _ at (0, 0) 198) f(x) = x at (-4, -20) A) y = 9x + 16 B) y = C) y = D) y = 198) _ B) y = -9x + 16 C) y = -7x - 16 D) y = -7x + 16 List the x-values in the graph at which the function is not differentiable 199) A) x = B) x = -1 C) x = 200) 199) _ D) x = 200) _ A) x = -2, x = 0, x = C) x = -3, x = B) x = -2, x = D) x = -3, x = 0, x = 201) 201) _ A) x = -2, x = 0, x = C) x = B) x = -2, x = D) x = 202) 202) _ A) x = C) x = 0, x = 1, x = B) x = D) x = 203) 203) _ A) x = C) x = 1, x = B) x = 1, x = 2, x = D) Function is differentiable at all points 204) 204) _ A) x = C) x = 2, x = B) Function is differentiable at all points D) x = 205) 205) _ A) x = -1, x = 0, x = C) x = -1, x = 206) B) x = D) Function is differentiable at all points 206) _ A) x = C) x = -2, x = 0, x = B) x = -2, x = D) Function is differentiable at all points 207) 207) _ A) x = 0, x = C) x = B) Function is differentiable at all points D) x = Solve the problem 208) Suppose that the cost, p, of shipping a 3-pound parcel depends on the distance shipped, x, according to the function p(x) depicted in the graph At what values is the function p not differentiable? A) B) C) D) Function is differentiable for all x in the domain 0, 3000 500, 3000 0, 500, 3000 209) Suppose that the cost, C, of producing x units of a product can be illustrated by the given graph At what values is the function C not differentiable? A) B) C) D) 208) _ 209) _ 100 Function is differentiable for all x in the domain 0, 100 0, 100, 200 210) Postal rates are $0.37 for the first ounce and $0.23 for each additional ounce (or fraction thereof) If x is the weight of function p not differentiable? a letter in ounces, then p(x) is the cost of mailing the letter, where p(x) = $0.37, if < x ≤ 1, p(x) = $0.60, if < x ≤ 2, p(x) = $0.83, if < x ≤ 3, and so on, up to 13 ounces The graph of p is shown below At what values is the 210) _ A) B) C) D) Function is differentiable for all x in the domain 0, 1, 2, 3, 4, 5, 6, 7, , 9, 10, 11, 12 0, 1, 2, 3, 4, 5, 6, 7, , 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, , 9, 10, 11, 12 211) In one city, taxicabs charge passengers $2.00 for entering a cab and then $0.40 for each one-quarter of a mile (or fraction thereof) that the cab travels (There are additional charges for slow traffic and idle times, but these are not considered here) If x is the distance traveled in miles, then C(x) is the cost of the taxi fare, where C(x) = $2.00, if x = 0, C(x) = $2.40, if < x < 0.25, C(x) = $2.80, if 0.25 ≤ x < 0.5, C(x) = $3.20, if 0.5 ≤ x < 0.75, and so on The graph of C is shown below 211) _ At what values is the function C not differentiable? A) 0.25, 0.5, 0.75, 1.0 B) Function is differentiable for all x in the domain C) 0.25, 0.5, 0.75 D) 0.25, 0.5, 0.75, 1.0, 1.25, 1.5 212) The graph shows the total sales in thousands of dollars from the distribution of x thousand catalogs At what values is the function not differentiable? A) B) C) D) Function is differentiable for all x in the domain 20, 30 10, 20, 40 10, 20, 30, 40, 50 213) The graph shows the population in millions of bacteria t minutes after a bactericide is introduced into a culture At what values of t is the function not differentiable? 212) _ 213) A) B) C) D) _ 3, 1, 2, 3, 4, Function is differentiable for all t in the domain Find f'(x) 214) 214) _ f(x) = A) B) f'(x) = - C) f'(x) = - D) f'(x) = - f'(x) = 215) 215) _ f(x) = A) B) f'(x) = C) f'(x) = - D) f'(x) = - f'(x) = 216) 216) _ f(x) = A) B) f'(x) = C) f'(x) = f'(x) = D) f'(x) = - 217) f(x) = A) 217) _ B) f'(x) = f'(x) = C) D) f'(x) = - f'(x) = 218) 218) _ f(x) = A) B) f'(x) = 219) f(x) = A) C) f'(x) = D) f'(x) = f'(x) = 219) _ B) f'(x) = C) f'(x) = f'(x) = D) f'(x) = 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39) 40) 41) 42) 43) 44) 45) 46) 47) 48) 49) 50) 51) D A A D C C B C A A A B A A B A A B B B D B B C C A C D A B A D B A D C B B B D D C C A B B D A C A A 52) 53) 54) 55) 56) 57) 58) 59) 60) 61) 62) 63) 64) 65) 66) 67) 68) 69) 70) 71) 72) 73) 74) 75) 76) 77) 78) 79) 80) 81) 82) 83) 84) 85) 86) 87) 88) 89) 90) 91) 92) 93) 94) 95) 96) 97) 98) 99) 100) 101) 102) 103) B B D C D B D A B B B A B B B A A B A B A B B A A A D B B C A D C D B A D C C A B A B B B A A B B B A A 104) 105) 106) 107) 108) 109) 110) 111) 112) 113) 114) 115) 116) 117) 118) 119) 120) 121) 122) 123) 124) 125) 126) 127) 128) 129) 130) 131) 132) 133) 134) 135) 136) 137) 138) 139) 140) 141) 142) 143) 144) 145) 146) 147) 148) 149) 150) 151) 152) 153) 154) 155) A C C D A A B A B A B C D D B A A D C D D A C B B B D B A C A D B C C A A A C B B A A C B B A B D D A B 156) 157) 158) 159) 160) 161) 162) 163) 164) 165) 166) 167) 168) 169) 170) 171) 172) 173) 174) 175) 176) 177) 178) 179) 180) 181) 182) 183) 184) 185) 186) 187) 188) 189) 190) 191) 192) 193) 194) 195) 196) 197) 198) 199) 200) 201) 202) 203) 204) 205) 206) 207) A A B A D B D C C C B C C A C D B B D A D A C C B A D C D A D D B B C A C A A A A D A A B C D D A B C A 208) 209) 210) 211) 212) 213) 214) 215) 216) 217) 218) 219) C A D D A D C C A A A B ... Yes B) No Evaluate or determine that the limit does not exist for each of the limits and for the given function f and number d 78) 78) f(x) = ; d = -1 A) (a) -5 (b) -3 (c) -3 C) (a) -5 (b)... function at the given points 82) f(x) = at x = -2 and x = -3 A) The function f is continuous at B) The function f is continuous at both but not at and 82) C) The function f is continuous at... f(x) = at x = -1 and x = A) The function f is continuous at neither B) The function f is continuous at both C) The function f is continuous at D) The function f is continuous at nor and but not at