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Chap2_Sec6

# Chap2_Sec6 - HORIZONTAL ASYMPTOTES An example of a curve...

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An example of a curve with two horizontal asymptotes is y = tan -1 x. s So, both the lines and are horizontal asymptotes. s This follows from the fact that the lines are vertical asymptotes of the graph of tan. 2 y π - = 2 y = 2 x = ± 1 1 lim tan lim tan 2 2 x x x x - - →-∞ →∞ = - = HORIZONTAL ASYMPTOTES

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Find the infinite limits, limits at infinity, and asymptotes for the function f whose graph is shown in the figure. HORIZONTAL ASYMPTOTES Example 1 (2.6)
and indicate which properties of limits are used at each stage. s As x becomes large, both numerator and denominator become large. s So, it isn’t obvious what happens to their ratio. s To evaluate the limit at infinity of any rational function, we first divide both the numerator and denominator by the highest power of x that occurs in the denominator. s We may assume that , since we are interested in only large values of x . 2

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Chap2_Sec6 - HORIZONTAL ASYMPTOTES An example of a curve...

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