In problem, using the table estimate the value of the limit
\(lim_{x\rightarrow{0}}{\sqrt{x+3}-\sqrt{3}\over x}\)

x	-0.1	-0.01	-0.001	0.001	0.01	0.1
f(x)	0.2911	0.2891	0.2886	0.2886	0.2885	0.28631

In problem, using the table estimate the value of the limit
\(lim_{x\rightarrow 0}{sin x\over x}\)

x	-0.1	-0.01	-0.001	0.001	0.01	0.1
f(x)	0.99833	0.99998	0.99999	0.99999	0.99998	0.99833

Compute \(lim_{x\rightarrow8}(5x)\)

Compute\(lim_{x\rightarrow-2}(-{3\over 2}x)\)

Find the positive integer n so that \(lim_{x\rightarrow 3}{x^n-3^n\over x-3}=27\)

Evaluate \(\lim _{ x\rightarrow a }{ \frac { \sqrt { x } +\sqrt { a } }{ x+a } } \)

Evaluate\(\lim _{ x\rightarrow 0 }{ \frac { \sqrt { 1+x } +\sqrt { 1-x } }{ 1+x } } \)

\(If\lim _{ x\rightarrow 2 }{ \frac { { x }^{ n }-{ 2 }^{ n } }{ x-2 } } =80\quad and\quad n\in N,\quad find\quad n.\)

Evaluate\(\lim _{ x\rightarrow 0 }{ \frac { { a }^{ x }-1 }{ { b }^{ x }-1 } } \)

For what value of k is the function \(f\left( x \right) =\begin{cases} \frac { \sin { 5x } }{ 3x } \quad if\quad x\neq 0 \\ k,\quad \quad \quad if\quad x=0 \end{cases}\) is continuous at x = 0.