Let's evaluate the limit:

\[
\lim_{x \to 0} x \csc x.
\]

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

\[
\lim_{x \to 0} x \csc x = \lim_{x \to 0} \frac{x}{\sin x}.
\]

We know from a standard trigonometric limit that:

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

Therefore, the limit

Explore the step-by-step solution for finding the limit of x csc(x) as x approaches 0. This problem covers key trigonometric and limit concepts, including the identity csc(x) = 1/sin(x) and the standard limit theorem for small x. Suitable for students in Grades 11-12 or early college.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation