# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\lim_{x\to0}\left(\frac{x\cdot \csc\left(2x\right)}{\cos\left(5x\right)}\right)$

Learn how to solve limits by direct substitution problems step by step online.

$\frac{0\csc\left(2\cdot 0\right)}{\cos\left(5\cdot 0\right)}$

Learn how to solve limits by direct substitution problems step by step online. Evaluate the limit of xcsc(2*x) as x approaches 0. Evaluate the limit by replacing all occurrences of x by 0. Simplifying. section:If the limit is undefined, we need to find the left side and right side limits. The limit is undefined.

$\frac{1}{2}$$\,\,\left(\approx 0.50000000003\right)$

### Problem Analysis

$\lim_{x\to0}\left(\frac{x\cdot \csc\left(2x\right)}{\cos\left(5x\right)}\right)$

### Main topic:

Limits by direct substitution

~ 0.06 seconds