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

Evaluate \(\lim _{ x\rightarrow 2 }{ \frac { { x }^{ 2 }-3x+2 }{ { x }^{ 2 }-x-2 } } \)

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.

Find \(\underset { x\rightarrow 1 }{ lim } \) fix), if  \(f(x)=\{ \begin{matrix} { x }^{ 2 }-1 & x\le 1 \\ -{ x }^{ 2 }-1 & x>1 \end{matrix}\)

Evaluate: \(\underset { x\rightarrow \infty }{ lim } \cfrac { \left( x+1 \right) ^{ 10 }+\left( x+2 \right) ^{ 10 }+...+\left( x+100 \right) ^{ 10 } }{ { x }^{ 10 }+{ x }^{ 10 } } \)