Find the vertical and horizontal asymptotes?

Question

Find all the vertical and horizontal asymptotes of the function f , justify with limits.

f(x)= (3e^(x))/(2-2e^(x))

Answer 1

Step 1 :

Definition :

The line is called a horizontal asymptote of the curve if either

Step 2 :

The function is .

Find vertical asymptote :

Vertical asymptotes exists when denominator is zero.

Equate denominator to zero.

Apply natural logarithm on each side.

The line is a vertical asymptote.

Step 3 :

Find horizontal asymptote :

The line is a horizontal asymptote.

The line is a horizontal asymptote.

Solution :

The vertical asymptote is .

The horizontal asymptotes are and .