Limits and Cont...

$$\displaystyle \lim _{ \theta \rightarrow 0 }{ \frac { 4\theta \left( \tan { \theta -2\theta \tan { \theta  }  }  \right)  }{ { \left( 1-\cos { 2\theta  }  \right)  }^{ 2 } }  } $$ is

$$\displaystyle\lim _{ x\rightarrow 0 }{ \dfrac { 3\sin { \left( { x }^{ 9} \right) -\sin { \left( { x }^{ 9 } \right)  }  }  }{ { x }^{ 3 } }  } =q$$

Let $$f(x)=(1+\sin x)^{\csc x}$$, the value of $$f(0)$$ so that $$f$$ is a continuous function is 

If $$k$$  is an integer such that $$\lim_{n \rightarrow \infty} \left[\left(\cos \dfrac{k\pi}{4}\right)^{2}-\left(\cos \dfrac{k\pi}{6}\right)^{2}\right]=0$$ then :

The value of $$\underset{x \rightarrow 0}{lim} \cos \,ec^4 \,x \displaystyle \overset{x^2}{\underset{0}{\int}} \dfrac{In(1 + 4t)}{1 + t^2}dt$$ is

$$\lim _ { x \rightarrow 0 } \left\{ \tan \left( \frac { \pi } { 4 } + x \right) \right\} ^ { \frac { 1 } { x } } =$$

If $$g(x)=\frac { x }{ \left[ x \right]  } for\quad x>2\quad then\quad \underset { x\rightarrow { 2 }^{ + } }{ Lim } \frac { g\left( x \right) -g\left( 2 \right)  }{ x-2 } $$

$$\lim_{n \rightarrow \infty}n^{2}\left(x^{1/n}-x^{1/\left(n+n\right)}\right),x>0$$, is equal to 

$$\lim_{x\rightarrow 0}\frac{ln(sin 3x)}{ln(sin x)}$$ is equal to

$$\underset{x \rightarrow 2}{lim} \dfrac{\sqrt[3]{60 + x^2} - 4}{\sin (x - 2)}$$ equals