MATH 1110 Quiz: MTH 1101 Quiz 4

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turquoisegnu128

9 Jan 2019

School

Northeastern University

Department

Mathematics

Course

MATH 1110

Professor

All

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Mth 1101 quiz 4 fall 1996. Instructions: put your name in the blanks above. Put your nal answers to each question in the designated spaces on these test pages. Show your work if there is not enough room, use the back of the page: list the elements in set s, where s is de ned by: 1 point each: 4 b, 4 / c, a b, b u, a, a (cid:1) . In a pollution study of 200 rivers: 58 were polluted by sulphates, 35 were polluted. 4 points: how many rivers were polluted by. 1 point each: at least two of these impurities, exactly one of these impurities, none of these impurities, the sox and the yanks are to play a best-of-three series, draw a tree diagram showing all the possible series. 4 points: list all the possible series, the number of possible 2-game series is:

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3. (20 pts) Let f be a differentiable one-to-one function on the interval (0,4) with the particular values of f and f' given in the table below, and let f-1 be the inverse function of f. Let g be the function given by the graph below. y y=g(x) 12 2 3 5 1 2 3 4 5 6 34-2 For (a), (b), and (c), circle the correct choice. lim 8(3+h) – g(3) h iii. 5 V. -2 vi. does not exist vii. none of the previous choices iv. O (b) dip [6^x +2)/(x) at x = 3 iii. 1 V. -1 vii. none of the previous choices iv. 0 vi. does not exist (0) [r_w) at x = 2 V. vii. none of the previous choices iv. I vi. does not exist (d) Consider the curve given by xey + y = f(x) - 1. Use implicit differentiation to computed at the point (2.0). Show your work.

6. On the axis below, sketch the graph of a continuous function y = f(:) having all of the following properties. Points are awarded for accuracy and neatness. [12 points) (i) f(0) = 3 and f(3) = 0 (ii) f'(-2) = f '(1) = 0 (iii) f is not differentiable at r=-1 (iv) [(x) > 0 for all & € (-0,3) (v) lim f(x) = 0 and lim,- S(:) = -1 (vi) F"(x) > 0 for all x € (-20, -3) and f "(c) < 0 for all 2 € (-1,2) (vii) (-3,2) is a point of inflection of f

1. (18 pts) The graph of a function f, defined on (-0, +o), is given in the figure below. - - y = f(x) - - - - - - N - - 4 A -2-1 144 -1 - - - - - - - -- - - -- Use the graph of f to answer questions (a)-(f) below. (a) Determine the value or write "does not exist". i. f(-3) = -2 ii. f(0) = 1 (b) Determine the limit or write "does not exist" (DNE). Write "does not exist" only if a limit does not exist and is not too or -0. i. lim f(x) = 0 iv. lim f(x) = +00 X- 3 x2 ii. lim f(x) = -4 v. lim f(x) = -0 X- 0- x -00 iii. lim f(x) = DNE vi. lim f(x) = -2 x0 x++00 (C) MULTIPLE CHOICE! Circle ONLY one answer! Find a number a for which the following statement is true (the function f is shown above): STATEMENT: The function f is continuous at a, and lim f(x) = 0. i. a=-3 iii. a=0 V. a=3 ii. a = -2 iv. a = 2 vi. Such a number does not exist. (d) Determine the largest intervals of continuity of f. Use interval notation to write your answer. (-0, -3), (-3,0), (0, 2), (2, +00) (e) Write the equation(s) of all vertical asymptotes of f. Write "none" if appropriate. x= 2 (f) Write the equation(s) of all horizontal asymptotes of f. Write "none" if appropriate. y = -2

MATH 1110 Quiz: MTH 1101 Quiz 4

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