MAT 21A Quiz: MAT21A Quiz 2 2014 Winter

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2 Oct 2018

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Name: (4 points) let y = f (x) be the function de ned on the interval [0, 4] whose graph is shown below. Evaluate the following limits (write dne if the limit does not exist). (a) lim x 1 f (x) = (b) lim x 2 f (x) = (c) lim x 3 f (x) = (d) lim x 3 1. 2 f (x) : (4 points) compute the following limits (write dne if the limit does not exist). The graph of y = f (x) (a) lim x 0 (b) lim t 1 (c) lim x 1 (d) lim h 0 x + 5 x2 + 3 t + 1 t2 1. 0 h: (2 points) determine if the following assertion is true or false, and explain its connection to a statement about limits. For any number > 0 there exists a number > 0 such that for any number x, if.

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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

20. Determine the following limits. Show all your work. If a limit does not exist indicate why with your work and write DNE. (a) (5 points) lim 500e -0.032 (b) (5 points) lim g(x) given that g(x) = (- 24 { 0 , 1 = 4 (2-5, r> 4

MAT 21A Quiz: MAT21A Quiz 2 2014 Winter

MAT 21A Full Course Notes

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