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Chapter 4: Q. 51 (page 225)

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.
R(x)=6x2+7x-53x+5

Short Answer

Expert verified

y=2x-1is the oblique asymptote of given rational expression.

Step by step solution

01

Step 1. Given information

Given rational expression:

R(x)=6x2+7x-53x+5

02

Step 2. Write the concept

If n = m + 1 (the degree of the numerator is one more than the degree of the denominator), the

quotient obtained is of the form ax + b (a polynomial of degree 1), and the line y = ax + b is an oblique

asymptote.

03

Step 3. Calculation

Here,n=2,m=1

Thus, n=m+1and therefore,

y=ax+bwillbeobliqueasymptote.y=2x-1

i.e. the quotient when we divide numerator with denominator.

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