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

Exercise

Find the limit

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

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