Find the horizontal, vertical, and oblique asymptotes of f(x) = 15x^ 2/ x 4 . Us

Question

Find the horizontal, vertical, and oblique asymptotes of f(x) = 15x^ 2/ x 4 . Use the information below to find the oblique asymptote. Oblique asymptote: Suppose p/q is a rational function where the degree of p is 1 greater than the degree of q. Using polynomial long division, p/q can be written as p(x)/ q(x) = mx + b + r(x)/ s(x) where r/s is a rational function with the property that r(x)/ s(x) 0 as x ±. This fact implies that p(x)/ q(x) mx + b when x is large. The line y = mx + b is an oblique (or slant) asymptote p/q.

Explanation / Answer

f(x) = 15x2/(x 4)

degree of numerator geater than degree of denominator , so no horizontal asymptote

vertical asympote occur when denominator=0

x-4 =0

=>x=4 is vertical asymptote

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for oblique asymptote

x-4 )...... 15x2 ........( 15x
..............15x2-60x
..........................................
.......................60x...............

f(x) = 15x2/(x 4) =15x +[60x/(x-4)]

from the given imformation m=15 , b=0

y =15x is the oblique asymptote

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