MATH 181A Lecture Notes - Lecture 11: Asymptote, Intermediate Value Theorem

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crimsontoad386

25 Oct 2017

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Problems marked with an asterisk (*) are particularly challenging and should be given careful consideration: consider the following graph of f . 3x (cid:5) 1 ax (cid:5) b x 2. Sample exam: find the vertical and horizontal asymptotes for f (cid:16)x(cid:17) (cid:7)(cid:98)a(cid:19)1 (cid:5) x(cid:19)1(cid:99)(cid:19)1. Classify the following statements as (a) always true (b) never true, or (c) true in some cases, false in others. Justify your answers. (a) f (cid:16)0(cid:17) (cid:7) 0 (b) for some x with (cid:19)1 (cid:110) x (cid:110) 1, f (cid:16)x(cid:17) (cid:7) 0. 2x 2 (a) let l (cid:7) lim x(cid:26)0 f (cid:16)x(cid:17). 138 lim x(cid:26)(cid:19)1 f (cid:16)x(cid:17) (cid:7) 1 using the - de nition: let f be the function whose graph is given below. 3 x (a) sketch a plausible graph of f (cid:41). _2 (b) sketch a plausible graph of a function f such that f(cid:41) (cid:7) f and f (cid:16)0(cid:17) (cid:7) 1.

Related Questions

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

5. (22 pts) x² - 4 x-5 if x < 2, Let g(x)= sin (1 x) if x 22. (I) Evaluate the limit or state that it does not exist. If the limit does not exist, explain why. Show your work. (Note: Possible answers include + cor -.) (a) (3 pts) lim g(x) = ; (b) (3 pts) lim g (x) = (II) (2 pts) Determine whether g has any horizontal asymptotes. If so, write the equation (or equations) of all horizontal asymptotes. (III) (4 pts) Determine whether g has any slant asymptotes. If so, write the equation (or equations) of all slant asymptotes. (IV) (2 pts) Determine whether g has any vertical asymptotes. If so, write the equation (or equations) of all vertical asymptotes. (V) (8 pts) Determine whether g is continuous at 2. Use the definition of continuity, when justifying your answer. SHOW YOUR WORK.

Please I need quick help these questions are due so soon. Thanks