# What is #lim_(x->oo) e^x/(x-1)# ?

If we evaluate this by direct substitution we get

L'Hospital's rule provides a solution for us. L'Hospital's rule states that:

Applying the rule,

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

Hence:

A little more formally:

Hence:

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

The limit of ( \frac{e^x}{x - 1} ) as ( x ) approaches infinity is infinity.

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

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.

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.

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.

- How to solve this limit?#lim_(n->oo)(1+x^n(x^2+4))/(x(x^n+1))#;x>0
- #y_n=log x_n, n =2,3,4,...and y_n-(n-1)/n y_(n-1)=1/n log n#, with #y_2=log sqrt2#, how do you prove that #x_n=(n!)^(1/n)#?
- How do you use the limit comparison test on the series #sum_(n=1)^oo(n^2-5n)/(n^3+n+1)# ?
- What is the interval of convergence of #sum ((x − 4)^n)/(n*(−9)^n)#?
- What is #int_(0)^(oo) 1/x^2sin(1/x) dx #?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7