Evaluate \(\lim _{ x\rightarrow 1 }{ \frac { \sqrt { { x }^{ 2 }-1 } +\sqrt { x-1 } }{ \sqrt { { x }^{ 2 }-1 } } } if\quad x>1\)

Evaluate \(\lim _{ x\rightarrow 1 }{ \frac { (2x-3)\sqrt { x } -1 }{ { 2x }^{ 2 }+x-3 } } \)

Examine the continuity of \(f\left( x \right) =\begin{cases} \frac { \sin { 2x } }{ \sin { 3x } } \quad if\quad x\neq 0 \\ 2\quad \quad \quad if\quad x=0 \end{cases}at\quad x=0\)

If \(f\left( x \right) =\frac { 2x+3\sin { x } }{ 3x+2\sin { x } } ,\quad x\neq 0\) is continuous at x = 0, then find f(0).

Evaluate \(\underset { x\rightarrow 0 }{ lim } f(x)\) ,where \(f(x)=\{ \begin{matrix} \frac { \left| x \right| }{ 0 } & x\neq 0 \\ 0 & x=0 \end{matrix}\)