Evaluate the limit of (sin x)^(tan x) as x approaches 0 from the right using L'Hôpital's rule.

Vault Of Euclid

Limit of (sin x)^(tan x) as x approaches 0 from the right

Limits core

Evaluate the limit: \[ \lim_{x\to 0^{+}} (\sin x)^{\tan x} \]

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

What you need first

Evaluating basic trigonometric limits
The chain rule for differentiation
Derivatives of trigonometric functions
Derivatives of logarithmic functions
L'Hôpital's rule
Properties of logarithms and exponents

What this problem tests

Tests the ability to recognize exponential indeterminate forms, apply logarithmic transformations, use L'Hôpital's rule, and simplify trigonometric expressions.

This is a standard calculus problem demonstrating how to handle the $0^0$ indeterminate form using logarithms and L'Hôpital's rule.

Limit of (sin x)^(tan x) as x approaches 0 from the right

What you need first

What this problem tests

More on Limits