Limits and Deri...

Let $$f$$ be a differentiable function such that $$f'(x) = 7- \dfrac{3}{4}\dfrac{f(x)}{x}, (x > 0)$$ and $$f(1) \neq 4$$.
Then $$\underset{x\to 0^+}{\lim} xf \left(\dfrac{1}{x}\right) $$:

$$\underset{x\to 0}{\lim} \left(\dfrac{3x^2+2}{7x^2+2}\right)^{1/x^2}$$ is equal to:

$$\lim _{ { x\rightarrow \pi /4 } } \dfrac { \cot ^{ { 3 } } x-\tan  x }{ \cos  (x+\pi /4) } $$  is

If $$f(x) = \begin{vmatrix} \cos x& x & 1\\ 2\sin x & x^{2} & 2x\ \\ \tan x & x & 1\end{vmatrix}$$, then $$\displaystyle \lim_{x\rightarrow 0} \dfrac {f'(x)}{x}$$.

$$\displaystyle \frac{d}{dx}\left(\frac{\sin x}{x}\right)$$

If $$x$$ is very large, then $$\dfrac {2x}{1+x}$$ is

If $$y=2  \sin  x -3x^4 + 8$$, then $$\dfrac{dy}{dx}$$ is

$$\displaystyle \lim_{x\rightarrow \infty} \sin x$$ equals

Derivative of $$2\tan x - 7\sec x$$ with respect to $$x$$ is:

$$\displaystyle \lim _{ x\rightarrow 0 }{ \cfrac { x{ e }^{ x }-\sin { x }  }{ x }  } $$ is equal to