Evaluate the limit of e^x / x^2 as x approaches 0, noting why L'Hôpital's rule does not apply.

Vault Of Euclid

Limit of e^x / x^2 as x approaches 0

Limits warmup

\(\lim_{x\to 0} \frac{e^x}{x^2}\)

The solution and a full step-by-step explanation are here. Sign in to read them.

What you need first

evaluating basic limits by substitution
knowing that e^0 = 1
understanding when a limit is infinite
knowing the conditions for L'Hôpital's rule

What this problem tests

Tests the ability to recognize non-indeterminate forms and evaluate infinite limits by analyzing signs.

This is a classic trap question in introductory calculus courses, designed to test whether students check the conditions for L'Hôpital's rule before applying it.

Limit of e^x / x^2 as x approaches 0

What you need first

What this problem tests

More on Limits