Limits and Cont...

f(X)=|x|+|x-1| is continuous at 

The value of $$\underset{x\rightarrow 1}{lim}(2-x)^{tan\left(\dfrac{\pi x}{2}\right)}$$ is

$$\displaystyle \lim_{x\rightarrow 0}\dfrac {\sin x - x}{x^{3}}$$ is equal to

$$\underset{x \rightarrow 1} {lim}\dfrac{x^2-1}{\sin^2x+\cos x\cos (x+2)-\cos^2(x+1)}$$ is-

$$\lim_{x\rightarrow 1}\frac{1-x^{-2/3}}{1-x^{-1/3}}$$

$$\overset {lim}{x \rightarrow \pi/2} \dfrac{\sin(x \ cos x)}{cos(x\, \ sin x)}$$ is equal to

$$\displaystyle \lim _{x \rightarrow 1}\left(\dfrac{x^{4}+x^{2}+x+1}{x^{2}-x+1}\right)^{\dfrac{1-\cos (x+1)}{(x+1)^{2}}} $$ is equal to:

 $$ \displaystyle \lim _{x \rightarrow 0}\left(\dfrac{1^{x}+2^{x}+3^{x}+\cdots+n^{x}}{n}\right)^{1 / x} $$ is equal to

If $$ \displaystyle \lim _{x \rightarrow 0} \dfrac{x^{n}-\sin x^{n}}{x-\sin ^{n} x} $$ is non-zero finite, then $$ n $$ must be equal

$$\displaystyle \lim _{x \rightarrow \infty} \dfrac{2+2 x+\sin 2 x}{(2 x+\sin 2 x) e^{\sin x}} $$ is equal to