# Step-by-step Solution

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## Step-by-step Solution

Problem to solve:

$\lim_{x\to0}\left(x\cdot\csc\left(3x\right)\right)$

Solving method

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

$\lim_{x\to 0}\left(\frac{\csc\left(3x\right)}{\frac{1}{x}}\right)$

Learn how to solve limits by direct substitution problems step by step online. Find the limit (x)->(0)lim(xcsc(3*x)). Rewrite the product inside the limit as a fraction. If we directly evaluate the limit \lim_{x\to 0}\left(\frac{\csc\left(3x\right)}{\frac{1}{x}}\right) as x tends to 0, we can see that it gives us an indeterminate form. We can solve this limit by applying L'Hôpital's rule, which consists of calculating the derivative of both the numerator and the denominator separately. After deriving both the numerator and denominator, the limit results in.

$\frac{1}{3}$$\,\,\left(\approx 0.3333333333333333\right)$
$\lim_{x\to0}\left(x\cdot\csc\left(3x\right)\right)$

### Main topic:

Limits by direct substitution

10. See formulas

~ 0.27 s