# Evaluate the following limits. lim_{xrightarrow0}frac{sin3x}{tan4x}

Evaluate the following limits.
$\underset{x\to 0}{lim}\frac{\mathrm{sin}3x}{\mathrm{tan}4x}$
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Evaluate the following limits.
$\underset{x\to 0}{lim}\frac{\mathrm{sin}3x}{\mathrm{tan}4x}$
To evaluate: $\underset{x\to 0}{lim}\frac{\mathrm{sin}3x}{\mathrm{tan}4x}$
Solution:
$\underset{x\to 0}{lim}\frac{\mathrm{sin}3x}{\mathrm{tan}4x}$
On simplifying further, we get:
$\underset{x\to 0}{lim}\frac{\mathrm{sin}3x}{\mathrm{tan}4x}=\underset{x\to 0}{lim}\frac{\frac{\mathrm{sin}\left(3x\right)}{\left(3x\right)}×\left(3x\right)}{\frac{\mathrm{tan}\left(4x\right)}{\left(4x\right)}×\left(4x\right)}$
$=\underset{x\to 0}{lim}\frac{\frac{\mathrm{sin}\left(3x\right)}{3x}}{\frac{\mathrm{tan}\left(4x\right)}{\left(4x\right)}}×\frac{3x}{4x}$
$\underset{x\to 0}{lim}\frac{1}{1}×\frac{3}{4}$
$=\frac{1}{1}×\frac{3}{4}$
$=\frac{3}{4}$
Result: $\underset{x\to 0}{lim}\frac{\mathrm{sin}3x}{\mathrm{tan}4x}=\frac{3}{4}$
Jeffrey Jordon