Vault Of Euclid

Limit of sin(x^2 - 1)/(x - 1) as x approaches 1

Limits warmup

\(\lim_{x\to 1} \frac{\sin (x^{2}-1)}{x-1}\)

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

What you need first

Evaluating limits by direct substitution
Recognizing indeterminate forms
L'Hôpital's rule
The chain rule for differentiation
Derivatives of trigonometric functions
Values of trigonometric functions at zero

What this problem tests

Tests the ability to recognize a 0/0 indeterminate form and correctly apply L'Hôpital's rule along with the chain rule.

This is a standard Calculus I problem testing the application of L'Hôpital's rule to trigonometric functions.

More on Limits

← today's set