Question

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

Limits and continuity
ANSWERED
asked 2021-02-04
Find the limit:
\(\lim_{t\rightarrow\infty}e^{3t}\sin^{-1}\frac{1}{t}\)

Answers (1)

2021-02-05
Given information:
The given function is \(\lim_{t\rightarrow\infty}e^{3t}\sin^{-1}\frac{1}{t}\)
Calculation:
Find the limit \(\lim_{t\rightarrow\infty}e^{3t}\sin^{-1}\frac{1}{t}\) as shown below:
\(\lim_{t\rightarrow\infty}e^{3t}\sin^{-1}\frac{1}{t}=e^{3(-\infty)}\sin^{-1}\frac{1}{-\infty}\)
\(=0\times\sin^{-1}(0)\)
\(=0(0)\)
\(=0\)
Thus, the limit \(\lim_{t\rightarrow\infty}e^{3t}\sin^{-1}\frac{1}{t}\) is 0.
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