olem $1$: Evaluate the following limits$.$

a$.\underset{x0}{lim}\frac{ln(1x)}{x}$

j$.\underset{x}{lim}{x}^{\frac{1}{x^2}}$

b$.\underset{x}{lim}\frac{x^5{5}^{x}10}{x^{10}10e5}$

k$.\underset{x1}{lim}(1lnx{)}^{(x-1{)}^{-1}}$

c$.\underset{x{0}^{}}{lim}xlnx$

$\underset{x{0}^{}}{lim}{x}^{sinx}$

d$.\underset{n}{lim}(1\frac{1}{n}{)}^{nx}$

m$.\underset{x0}{lim}(cosx{)}^{\frac{3}{x^2}}$

e$.\underset{x}{lim}(1\frac{1}{x}{)}^{x^2}$

n$.\underset{x0}{lim}\frac{si{n}^{-1}(x)}{x}$

f$.\underset{x}{lim}(1\frac{1}{x^2}{)}^x$

a$.\underset{x}{lim}(\frac{x}{x1}{)}^x$

g$.\underset{x0}{lim}(cotx-\frac{1}{x})$

p$.\underset{x0}{lim}\frac{ta{n}^{-1}(x)}{si{n}^{-1}(x)}$

h$.\underset{x}{lim}(ln(1x^2)-ln(5x^{2}x1))$

q$.\underset{x1}{lim}\frac{ta{n}^{-1}(x)-\frac{}{4}}{tan(\frac{x}{4})-1}$

i$.\underset{x1}{lim}tan(\frac{x}{2})lnx$

Note: the symbol