Math Problem Statement

limx->0 xcscx

Solution

Let's evaluate the limit:

limx0xcscx.\lim_{x \to 0} x \csc x.

Recall that cscx=1sinx\csc x = \frac{1}{\sin x}, so the expression can be rewritten as:

limx0xcscx=limx0xsinx.\lim_{x \to 0} x \csc x = \lim_{x \to 0} \frac{x}{\sin x}.

We know from a standard trigonometric limit that:

limx0xsinx=1.\lim_{x \to 0} \frac{x}{\sin x} = 1.

Therefore, the limit

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Limits

Formulas

csc x = 1 / sin x
lim x -> 0 (x / sin x) = 1

Theorems

Standard Limit Theorem for sin x as x approaches 0

Suitable Grade Level

Grades 11-12 or Early College