Evaluate the following limits :\(lim_{x\rightarrow 0}{sin \alpha x\over sin \beta x}\)

Evaluate the following limits :\(lim_{x\rightarrow 0}{2^x-3^x\over x}\)

Evaluate the following limits :\(\)\(lim_{x \rightarrow \infty}\{ x[log(x+a)-log(x)]\}\)

Evaluate the following limits :\(lim_{x\rightarrow {\pi\over 2}}(1+sin x)^{2cosec \ x}\)

Evaluate the following limits :\(lim_{x\rightarrow 0}{\sqrt{2}-\sqrt{1+cos x}\over sin^2x}\)

Evaluate the following limits :\(lim_{x\rightarrow 0}{tan \ x-sin x\over x^3}\)

Describe the interval(s) on which each function is continuous.
\(g(x)= \begin{cases}\sin \frac{1}{x}, & x \neq 0 \\ 0, & x=0\end{cases}\)

Find the points of discontinuity of the function f, where f(x)={\(\begin{matrix} 4x+5, & if\quad x\le 3 \\ 4x-5, & if\quad x>3 \end{matrix}\)

Find the points of discontinuity of the function f, where
f(x) = {\(\begin{matrix} x+2, & if\quad x\ge 2 \\ { x }^{ 2 }, & if\quad x<2 \end{matrix}\)

If f and g are continuous functions with f(3) = 5 and \(lim_{x\rightarrow3}[2f(x)-g(x)]=4\), find g(3).