( lim _{n rightarrow infty} frac{5 n^{2}-sin (3 n)}{n^{2}+10} )

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Step:1 ：( lim _{n rightarrow infty} frac{5 n^{2}-sin (3 n)}{n^{2}+10} cong lim _{n rightarrow infty} frac{5 n^{2}}{n^{2}} )Step:2 ：( lim _{n rightarrow infty} frac{n^{2}(5-frac{sin (3 n)}{n^{2}})}{n^{2}(1+frac{10}{n^{2}})} cong lim _{n rightarrow infty} frac{(5-frac{sin (3 n)}{n^{2}})}{(1+frac{10}{n^{2}})} )Step:3 ：( lim _{n rightarrow infty} frac{5 - 0}{1 + 0} )

Answer

Step: 1 ：( lim _{n rightarrow infty} frac{5 n^{2}-sin (3 n)}{n^{2}+10} cong lim _{n rightarrow infty} frac{5 n^{2}}{n^{2}} )Step: 2 ：( lim _{n rightarrow infty} frac{n^{2}(5-frac{sin (3 n)}{n^{2}})}{n^{2}(1+frac{10}{n^{2}})} cong lim _{n rightarrow infty} frac{(5-frac{sin (3 n)}{n^{2}})}{(1+frac{10}{n^{2}})} )Step: 3 ：( lim _{n rightarrow infty} frac{5 - 0}{1 + 0} )

\( \lim _{n \rightarrow \infty} \frac{5 n^{2}-\sin (3 n)}{n^{2}+10} \)

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