CalcNotes0204-page6

CalcNotes0204-page6 - (Section 2.4: Limits and Infinity II)...

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(Section 2.4: Limits and Infinity II) 2.4.6 Finding VAs for Graphs of Rational Functions (Expressed in Simplified Form) If: fx () is rational and written in the form = Nx Dx , and are polynomials, ± 0 (i.e., the zero polynomial), and and have no real zeros in common; i.e., they have no variable factors in common. Then: The graph of y = has a VA at x = a (and lim x ± a + = ² or ³² , and lim x ± a ² = ³ or ²³ ) ± a is a real zero of . Example 4 (Revisiting Example 3) Let = x + 1 x 2 + 4 x . Find the equations of the vertical asymptotes (VAs) of the graph of y = in the xy -plane. Justify your answer using limits. Solution Method x + 1 x 2 + 4 x = x + 1 xx + 4 . Observe that the numerator and the denominator have no variable factors (and no real zeros) in common. Therefore,
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This note was uploaded on 12/29/2011 for the course MATH 150 taught by Professor Sturst during the Fall '10 term at SUNY Stony Brook.

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