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# Ap calculus warm up 8.27.13

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### Ap calculus warm up 8.27.13

1. 1. AP Calculus Warm up
2. 2. Limits at infinity • How do you find the limit of a function when x approaches +/- infinity? – YOU FIND THE HORIZONTAL ASYMPTOTES Tells you the end behavior of the graph.)(lim xf x
3. 3. How do we find the horizontal asymptotes? • Compare the degrees of the numerator and denominator. Degrees equal: It’s the ratio of the leading coefficients. Degree of numerator is greatest: No asymptote. The function is unbounded at the ends. (Goes on forever to infinity) Degree of denominator is greatest: y = 0 (x-axis) is horizontal asymptote
4. 4. Rational functions • Rational functions are fractions of 2 polynomials. • They may have vertical or horizontal asymptotes.
5. 5. Example 1 12 lim x x x
6. 6. Example 13 52 lim 2 x x x
7. 7. Example 13 52 lim 2 3 x x x
8. 8. Practice Evaluate each limit xx 1 lim 13 23 lim 2 x x x 13 25 lim 4 4 x xx x