Vault Of Euclid

Limit of sin(2x) over 2x^2 + 3x as x approaches 0

Limits warmup

\(\lim_{x\to 0} \frac{\sin 2x}{2x^{2}+3x}\)

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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
Derivatives of polynomials

What this problem tests

Tests the ability to recognize indeterminate forms and correctly apply L'Hôpital's rule along with the chain rule.

This is a standard introductory calculus problem demonstrating the application of L'Hôpital's rule to trigonometric functions.

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