MAT 16A Final: MAT_16A_FQ2017 Exam

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turquoisegnu128

9 Jan 2019

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Final exam (1) based on the graph below, label each of the following as either + (positive), - (negative), 0 (zero), or dne (does not exist). (40 points) lim x 2 f (x) f ( 2) f (3) lim x 2+ f (x) f ( 2) f (3) f ( 2) f (3) 2 (2) evaluate each of the following limits. (40 points) (a) lim x 3 x3 + 2x2 x + 3. X2 + 3 2 x 1 (c) lim x 1 px2 + 8x. 4 (3) find the derivative of each of the following functions. (40 points) (a) f (x) = 3x5. 1 x (b) f (x) = (sin(x) + cos(x))3 (c) f (x) = x3. 5 (d) f (x) = (5x + 7)px2 + 2x + 2. 6 (4) find the equation for the tangent line to the given function at the speci ed point. (10 points) f (x) = 2 x2.

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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

1. (20 pts) The graph of a function f is given in the figure below. Use the graph of f to answer the questions below. y = f(x) -64 - - - - - - - - - - - - (I) (1 pt) Pind the domain of f. Domain of f = (-0, 3) U (3, +co) (II) (1 pt) Find the range of f. Range of f = (-, +O) (a) (1 pt) lim f (x) = 0 (b) (1 pt) f(3) = DNE (does not exist) (c) (1 pt) f (5) = 2 (a) (1 pt) lim f (x) = 0 (0) (1 pt) lim f (x) = -- (f) (1 pt) lim f (x) = DNE 0 1 (g) (1 pt) lim f (x) = + (h) (1 pt) lim f (x) = -6 X-++00 (IV) (2 pts) Find all vertical asymptotes. (V) (2 pts) Find all horizontal asymptotes. (VI) (6 pts) Determine the intervals of continuity for f. (-0, 0], (0, 3), (3, 5), (5, +00)

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MAT 16A Final: MAT_16A_FQ2017 Exam

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