# Find the limit: lim_{trightarrowinfty}e^{3t}sin^{-1}frac{1}{t}

Find the limit:
$\underset{t\to \mathrm{\infty }}{lim}{e}^{3t}{\mathrm{sin}}^{-1}\frac{1}{t}$
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berggansS
Given information:
The given function is $\underset{t\to \mathrm{\infty }}{lim}{e}^{3t}{\mathrm{sin}}^{-1}\frac{1}{t}$
Calculation:
Find the limit $\underset{t\to \mathrm{\infty }}{lim}{e}^{3t}{\mathrm{sin}}^{-1}\frac{1}{t}$ as shown below:
$\underset{t\to \mathrm{\infty }}{lim}{e}^{3t}{\mathrm{sin}}^{-1}\frac{1}{t}={e}^{3\left(-\mathrm{\infty }\right)}{\mathrm{sin}}^{-1}\frac{1}{-\mathrm{\infty }}$
$=0×{\mathrm{sin}}^{-1}\left(0\right)$
$=0\left(0\right)$
$=0$
Thus, the limit $\underset{t\to \mathrm{\infty }}{lim}{e}^{3t}{\mathrm{sin}}^{-1}\frac{1}{t}$ is 0.
Jeffrey Jordon