Home > Algebra > Excluded Values for Rational Expressions

What are the asymptote(s) and hole(s), if any, of # f(x) =e^x/(x(x-e)(x-1)#?

Answer 1

To find the asymptotes, look for restrictions in the equation. In this question, the denominator can not be equal to 0, so set each factor equal to 0 to find the asymptotes.

#x=0#, #x-e=0#, #x-1=0# #x=0#, #x=e#, #x=1#

Your VAs are 0, e, and 1

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Hazel Anglin

The function f(x) = e^x/(x(x-e)(x-1) has vertical asymptotes at x = 0, x = e, and x = 1. There is a hole at x = e.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.