# Step-by-step Solution

## Find the limit of $x\csc\left(2x\right)$ as $x$ approaches $0$

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### Videos

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## Step-by-step explanation

Problem to solve:

$\lim_{x\to0}\left(\frac{x\cdot \csc\left(2x\right)}{\cos\left(5x\right)}\right)$
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Evaluating the limit when $x$ tends to $0$

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

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### Problem Analysis

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

### Main topic:

Limits by direct substitution

~ 0.28 seconds