MAT 211 Lecture Notes - Lecture 6: Classification Of Discontinuities, Joule, Intermediate Value Theorem

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plummoose320

20 Jan 2018

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Provide a generalization to each of the key terms listed in this section. If a function does not support all three of those tests, then that function is not continuous, which is also known as the function being discontinuous when x = a. Since that is the proper case, then for any given > 0, you would be able to nd out that > 0, which can be explained by the following (along with f is continuous at a ): |x a| < is implying that. An in nite discontinuity is a discontinuity that occurs when the limit of a function being in nite or equaled to . A jump discontinuity is a discontinuity that occurs when you have unequal sides; if the left side of a limit does not equal the right side of the limit, then this would be a jump discontinuity.

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Can you please help me with number 5?

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bluebee563

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

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