# 2019W1MATH100V01.XFOGAQDUTM02.A5

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Yue Shi 2019W1 MATH 100 V01 Assignment A5 due 10/18/2019 at 09:00am PDT 1. (1 point) Use the given graph of the function to find the x -values for which f is discontinuous. Answer (separate by commas): x = Note: You can click on the graph to enlarge the image. Answer(s) submitted: -3,-4,2,4 (incorrect) 2. (1 point) Why is the following function discontinuous at x = 1? f ( x ) = 8 > < > : 1 + x 2 if x < 1 4 - x if x 1 (a) f ( 1 ) does not exist. (b) lim x ! 1 f ( x ) does not exist (or is infinite). (c) Both (a) and (b). (d) f ( 1 ) and lim x ! 1 f ( x ) exist, they are not equal. Answer(s) submitted: d (incorrect) 3. (1 point) Why is the following function discontinuous at x = 1? f ( x ) = 8 > > < > > : 1 x - 1 if x 6 = 1 2 if x = 1 (a) f ( 1 ) does not exist. (b) lim x ! 1 f ( x ) does not exist (or is infinite). (c) Both (a) and (b). (d) f ( 1 ) and lim x ! 1 f ( x ) exist, but they are not equal. Answer(s) submitted: b (correct) 4. (1 point) Why is the following function discontinuous at x = - 6? f ( x ) = 8 > > < > > : x 2 + 7 x + 6 x + 6 if x 6 = - 6 8 if x = - 6 (a) f ( - 6 ) does not exist. (b) lim x !- 6 f ( x ) does not exist (or is infinite). (c) Both (a) and (b). (d) f ( - 6 ) and lim x !- 6 f ( x ) exist, but they are not equal. Answer: ? Answer(s) submitted: b (incorrect) 5. (1 point) Use interval notation to indicate where f ( x ) = x - 7 ( x - 2 )( x + 1 ) is continuous. f is continuous on Answer(s) submitted: (-Inf,-1)U(-1,2)U(2,Inf) (correct) 6. (1 point) If f and g are continuous functions with f ( 0 ) = 3 and lim x ! 0 f ( x ) g ( x ) = 6, find g ( 0 ) . g ( 0 ) = Answer(s) submitted: 2 (correct) 1
7. (1 point) For what value of the constant c is the function f continuous on the interval ( - , ) . f ( x ) = ( x 2 - 10 , x c 4 x - 14 , x > c c = Answer(s) submitted: 2 (correct) 8. (1 point) For what value of the constant c is the function f continuous on the interval ( - , ) . f ( x ) = ( cx 2 + 4 x , x < 2 x 3 - cx , x 2 c = Answer(s) submitted: 0 (correct) 9. (1 point) What values of a and b make the function f continuous everywhere? f ( x ) = 8 > > < > > : x 2 - 4 x - 2 , if x < 2 ax 2 - bx - 18 , if 2 x < 3 12 x - a + b , if x 3 a = and b = Answer(s) submitted: 5 -1 (correct) 10. (1 point) The table below gives for the value of contin- uous function f at each x -value. Using the Intermediate Value Theorem and the information in the table, determine the small- est interval in which the function must have a root. x f ( x ) - 5 1 . 25 - 4 2 . 03 - 3 3 . 05 - 2 3 . 01 - 1 1 . 02 0 - 0 . 69 1 - 2 . 43 2 - 3 . 45 3 - 6 . 76 4 - 7 . 93 5 - 7 . 93 Answer (in interval notation): Answer(s) submitted: (-1,0) (correct) Generated by c WeBWorK, http://webwork.maa.org, Mathematical Association of America 2
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