Problem

\( \lim _{n \rightarrow \infty} \frac{n^{2}\left(\sin n+\cos ^{3} n\right)}{\left(n^{2}+1\right)(n-3)} \)

Solution

Step 1 :\( \lim _{n \rightarrow \infty} \frac{n^{2}\left(\sin n+\cos ^{3} n\right)}{\left(n^{2}+1\right)(n-3)} = \frac{\infty}{\infty} \)

Step 2 :\( \lim _{n \rightarrow \infty} \frac{n^{2} \sin n}{(n^{2}+1)(n-3)} + \lim _{n \rightarrow \infty} \frac{n^{2} \cos^{3} n}{(n^{2}+1)(n-3)}\)

Step 3 :\(\lim _{n \rightarrow \infty} \frac{n^{2}\left(\sin n+\cos ^{3} n\right)}{\left(n^{2}+1\right)(n-3)} = 0 + 0\)

From Solvely APP
Source: https://solvelyapp.com/problems/21359/

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