Problem

\( \lim _{n \rightarrow \infty}\left(\sqrt{n^{2}+5 n}-\sqrt{n^{2}+n}\right) \)

Answer

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Answer

\(\lim_{n\rightarrow\infty} \frac{4}{\frac{\sqrt{n^2+5n}}{n}+\frac{\sqrt{n^2+n}}{n}}\)

Steps

Step 1 ：\(\lim_{n\rightarrow\infty} \frac{(n^2+5n)-(n^2+n)}{\sqrt{n^2+5n}+\sqrt{n^2+n}}\)

Step 2 ：\(\lim_{n\rightarrow\infty} \frac{4n}{\sqrt{n^2+5n}+\sqrt{n^2+n}}\)

Step 3 ：\(\lim_{n\rightarrow\infty} \frac{4}{\frac{\sqrt{n^2+5n}}{n}+\frac{\sqrt{n^2+n}}{n}}\)

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