Question

Identify the oblique asymptote of f(x)=x+4/3x^2+5x-2

Answer 1

No oblique asymptote

Explanation:

To find the oblique asymptote of f(x)

`f(x) = (x+4)/(3x^2+5x-2)`

Here numerator has degree 1 and denomintor degree 2

Degree of numerator < Degree of denominator

Hence there is no oblique asymptote

When the degree of the denominator > that of the numerator, we saw that the value in the denominator got so much bigger, so quickly, giving us a horizontal asymptote of the x-axis. Or we can write

f(x) = a polynomial of x + a proper fraction.

In this case only we have oblique asymptotes but not when numerator has less degree.