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# P08Ans - x = 0 e How must you redeﬁne the function at...

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Project 8 MAC 2233 1. Examine the function: f ( x ) = x 2 - x - 2 4 x 2 - 2 x 3 a) What type of function is this? What is the domain of the function? What are its discon- tinuities? rational function; discontinuities at x = 0 , 2 b) Evaluate the right and left limits at each discontinuity: x = 0 : right limit is -∞ ; left limit is -∞ x = 2 : right limit is -3/8; left limit is -3/8 c) Evaluate the limits at infinity for the function. limit toward and -∞ are both 0 d) Complete the statements: f ( x ) has a removable discontinuity at the x -value(s): x = 2 f ( x ) has a nonremovable discontinuity at the
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Unformatted text preview: x = 0 e) How must you redeﬁne the function at your removable point(s) of discontinuity in order to make the function continuous there? Deﬁne f (2) =-3 / 8 2. Try to draw the graph of a function having the following properties: It is deﬁned for all real x ; the limit at x = 2 exists, but f is discontinuous there; the limit at x =-2 does not exist, but the right and left limits do; the limits at inﬁnity both exist, but are different; f has an inﬁnite discontinuity at x = 0 ....
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