6. Show that (a) \( \lim \left(\frac{1}{\sqrt{n+7}}\right)=0 \) (b) \( \lim \left(\frac{2 n}{n+2}\right)=2 \), (c) \( \lim \left(\frac{\sqrt{n}}{n+1}\right)=0 \), (d) \( \lim \left(\frac{(-1)^{n} n}{n^{2}+1}\right)=0 \).
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Step 1: Consider the limit \( \lim_{n \to \infty} \left(\frac{1}{\sqrt{n+7}}\right) \). Show more…
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