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

\(It\quad \lim _{ x\rightarrow a }{ \frac { { x }^{ 9 }-{ a }^{ 9 } }{ x-a } } =9,\)find all possible values of a.

Evaluate \(\lim _{ x\rightarrow \pi }{ \frac { \sin { x } }{ x-\pi } } \)

Suppose \(f(x)=\{ \begin{matrix} a+bx, & x<1 \\ 4, & x=1 \\ b-ax & x>1 \end{matrix}\) and,if \(\underset { x\rightarrow 1 }{ lim } f(x)=f(1)\) .What are possible values of a and b?

Evaluate \(\underset { x\rightarrow \infty }{ lim } \left( \sqrt { { x }^{ 2 }-x+1 } +x \right) \)