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Calculating Limit of Series – A quotient of polynomials and trigonometric functions – Exercise 716

Exercise

Find the limit

\lim _ { n \rightarrow \infty}\frac{2 n^4 \arccos {(\frac{1}{n})}+n^2\sin{(n)}}{7n^4+3n^2+5}

Final Answer


\lim _ { n \rightarrow \infty}\frac{2 n^4 \arccos {(\frac{1}{n})}+n^2\sin{(n)}}{7n^4+3n^2+5}=\frac{\pi}{7}

Solution

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