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May 29, 2018 · Note that it only requires one of the above limits for a function to have a vertical asymptote at \(x = a\). Using this definition we can see that the first two examples had vertical asymptotes at \(x = 0\) while the third example had a vertical asymptote at \(x = - 2\).

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12 There are no zeros, a hole exists at x = –3/2, vertical asymptote is at x = 1, and horizontal asymptote is at y = 0. 13. There is a zero at 6, a hole exists at x = –3, no vertical asymptotes, and horizontal asymptote at y = x – 6.

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Notice that the vertical asymptote has also shifted \(3\) units to the right, to \(x = 3\), but the horizontal asymptote, \(y = 0\) has stayed in the same place. Moving it to the left. To move the reciprocal graph \(a\) units to the left, add \(a\) to \(x\) to give the new function: \(f(x) = \dfrac{1}{x + a}\).

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View WS07_sol.pdf from MATH TRIGONOMET at University of Illinois, Urbana Champaign. SOLUTIONS Group: + + + your Name: Math 220. Worksheet 7. 09/17/20 Limits at infinity and asymptotes 1. Give an

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Aug 16, 2014 · Find the vertical asymptotes and holes for the graph of each rational function. 5. 2 5 1 x y x 6. 2 2 2 x 7. ( 1) x y xx 8. 2 3 9 x y x 9. 2 ( 2)( 2) x y xx y 10. 2 2 4 4 x x 11. 2 25 4 x y x 12. ( 2)(2 3) (5 4)( 3) xx y xx Find the horizontal asymptote of the graph of each rational function. 13. 2 6 y x 14. 2 4 x y x 15. 2 2 23 6 x y x 16. 2 3 ...

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Jan 24, 2018 · Here is a set of practice problems to accompany the Infinite Limits section of the Limits chapter of the notes for Paul Dawkins Calculus I course at Lamar University.

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Section 2.6: Limits at in nity, horizontal asymptotes Theory: We want to describe what happens to the function values y = f(x) if x gets bigger and bigger (we say x is approaching +1) or smaller and smaller (approaching 1 ). It is possible that f(x) approaches a nite value. The exact de nition can be stated as follows: De nition 1