Evaluate:\(lim_{x\rightarrow{3}}{x^2-9\over x-3}\) if it exists by finding f(3^-)and f(3⁺).

Verify the existence of \(lim_{x\rightarrow1}f(x),\) where \(f(x)= \begin{cases}\frac{|x-1|}{x-1}, & \text { for } x \neq 1 \\ 0, & \text { for } x=1\end{cases}\)

Calculate \(lim_{x\rightarrow3}{(x^2-6x+5)\over x^3-8x+7}\)

Find \(lim_{t\rightarrow0}{\sqrt{t^2+9}-3\over t^2}.\)

Find the relation between a and b if \(lim_{x\rightarrow3}f(x)\) exists where \(f(x)= \begin{cases}a x+b & \text { if } x>3 \\ 3 a x-4 b+1 & \text { if } x<3\end{cases}\)

Evaluate the following limits :
\(lim_{\sqrt x\rightarrow3}{x^2-81\over \sqrt x-3}\)

Evaluate the following limits :
\(lim_{x\rightarrow2}{{1\over x}-{1\over2}\over x-2}\)

Calculate \(lim_{x\rightarrow0}{1\over (x^2+x^3)}\)

Evaluate \(lim_{x\rightarrow 2}{1\over (x-2)^3}\)

\(f(x)=tan \ x \ at \ x={\pi\over 2}.\)