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Class Note for MATH 1330 at UH


Class Note for MATH 1330 at UH

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This 3 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 21 views.

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Date Created: 02/06/15
How to nd a Horizontal Asymptote Given a rational function how do you know if there s a horizontal asymptote The Procedure 0 Check the highest power of X in the numerator 7 call it n 0 Check the highest power of X in the denominator 7 call it d 0 Now look at the ratio of n to d in other words make a fraction with n in the numerator and d in the denominator You will need to note the size of the fraction nd gt 1 nd l ndltl if nd is bigger than 1 then there is no horizontal asymptote you will nd out later that there might be a kind of asymptote called an oblique asymptote but no horizontal one 5X5 X3 2 5 for example 2 7 gt 1 no hor1zontal asymptote 3X X l 2 if nd is one then the asymptote is the ratio of the coef cients in the natural order 5X2 X3 2 2 5 foreXam le 71 HA is 7 p 3X2X l 2 y 3 if nd is less than one then the horizontal asymptote is the x axis 5X2 X3 2 2 for eXample 5 7 lt 1 HA is y 0 the X aXis 3X X l 5 Practice 7 nd the HA horizontal asymptote If there is none write none else write the asymptote as an equation 1 X3 39 2x 11 25X3 11X2 5 2 2 X 25 3 3X2 9X2 81 Answers 1 1 7 y 2 2 none Slant Asymptotes You graph an asymptote that is a line if the power in the numerator is exactly one higher than the power in the denominator To nd the line actually do the diVision 7 long diVision of the denominator into the numerator You will get a quotient of the form mx b remainder mX b is the slant asymptote Example 2 x 10X 7X2 2X 3 5X4 2X 3 10X2 7X 2 with a remainder the asymptote line is 5 4 6X27Xl You try it with fX 2Xl answer 3X 2 is the slant asymptote


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