1. Find the limit of the following sequences. \text { (a) } \lim _{n \rightarrow \infty} \frac{\sqrt{n}+1}{n^{3}+n+2} \text { (b) } \lim _{n \rightarrow \infty} \frac{\sqrt[4]{n^{7}+c}}{\sqrt{n^{5}+1}+n+2} \text { where }

c>0 \text { is a constant } \text { (c) } \lim _{n \rightarrow \infty} \frac{n^{3}+(-1)^{n}}{2 n^{3}+n^{2}+1} \text { (d) } \lim _{n \rightarrow \infty} \frac{\sqrt{n}+1}{n^{c}+2 n+4} \text { where } c>3 \text { is a constant } \text { (e) } \lim _{n \rightarrow \infty} \frac{\sqrt[n]{2}+1}{n+2} \text { (f) } \lim _{n \rightarrow \infty} \frac{\sqrt{n}+1}{c^{n}+2} \text { where } c>1 \text { is a constant } \text { (g) } \lim _{n \rightarrow \infty} \frac{\sin (n)+c}{n^{2}+2 n+2} \text { where } c>1 \text { is a constant } \text { (h) } \lim _{n \rightarrow \infty}\left(2+\frac{1}{n}\right)^{n} \text { (i) } \lim _{n \rightarrow \infty}\left(\frac{1}{2}+\frac{1}{n}\right)^{n} \text { (j) } \lim _{n \rightarrow \infty}\left(1+\frac{2}{n}\right)^{n} \text { (k) } \lim _{n \rightarrow \infty} \frac{\ln \left(n^{3}\right)}{n^{c}} \text { where } c>1 \text { is a constant }