Calculus Examples

$f (x) = \frac{e^{- 2 x}}{x - 5}$

Step 1

Find where the expression $\frac{e^{- 2 x}}{x - 5}$ is undefined.

$x = 5$

Step 2

Since its numerator approaches a real number while its denominator is unbounded, the fraction $\frac{e^{- 2 x}}{x - 5}$ approaches $0$ .

$0$

Step 3

List the horizontal asymptotes:

$y = 0$

Step 4

There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.

No Oblique Asymptotes

Step 5

This is the set of all asymptotes.

Vertical Asymptotes: $x = 5$

Horizontal Asymptotes: $y = 0$

No Oblique Asymptotes

Step 6