Limits and Deri...

Use limit properties to evaluate $$\displaystyle\lim_{x\to4}\dfrac{3x^2\tan \dfrac {\pi}{x}}x $$

Evaluate $$\underset{x \rightarrow 3}\lim \sqrt[4] {x^3}$$ using the properties of limits.

What is $$\displaystyle\lim _{ x\rightarrow 0 }{ \frac { \cos { x }  }{ \pi -x }  } $$ equal to?

Find $$\dfrac{dy}{dx}$$ of function $$y= e^{x^3} +\dfrac{1}{2} \log x $$

Differentiate: $$x^{100} + \sin x - 1$$

Consider the differential equation $$\frac { d y } { d x } = \cos x$$ Then we observe that 

$$x^{\frac{1}{2}} + 1=  t$$
differentiate w.r.t. x

$$\lim_{x\rightarrow\ 0}\dfrac{\sin7x}{\sin3x}$$ equals

If a sequence $$< a_{n} >$$ is such that $$a_{1},a_{n+1}=\dfrac {2+3a_{n}}{1+2a_{n}}$$ and $$\displaystyle \lim_{n \rightarrow \infty}a_{n}$$ exists, then $$a_{n}$$ is equal to

Evaluate the following limit :