MAT237Y1 Lecture Notes - Negative Number, Asymptote

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raspberrysardine362

4 Jan 2013

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Continuity: graph is connected with no breaks or holes. Continuity at x = c occurs if all three of the following are true: 2. ) is defined. (there are no vertical asymptotes or holes at xf x . 0x exists. (if it didn"t exist, then there must be a break in the graph or a vertical asymptote. ) Section 2. 5 notes page 1 ( 0xf lim x x lim x x. 0x xf xf (i can plug in for x since there is not a hole). Let"s look at the below graph from the previous section. We see that the graph will be discontinuous at x = -2, 0, 2, and 4. The value of should be assigned to f(2) to make it continuous. For all these problems you want to look for any place where the equation will be undefined. This only occurs if you are dividing by a negative number or taking the even root of a negative number.

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tealturtle320

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

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bluebee563

MAT237Y1 Lecture Notes - Negative Number, Asymptote

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