Question

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

Limits and continuity
Find the limit:
$$\lim_{t\rightarrow\infty}e^{3t}\sin^{-1}\frac{1}{t}$$

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.