Application of ...

Which of the following statements is/are correct ?

$$f(x)$$ is differentiable function satisfying the relation $$f(x)=x^{2}+\displaystyle \int^{x}_{0}e^{-t}f(x-t)dt$$, then $$\displaystyle \sum^{9}_{k=1}f(k)$$ equals

$$f(x)=\frac{x}{log x}-\frac{log}{x}$$ is increasing in 

If $$y = \log _ { \sin x } ( \tan x ) ,$$ then $$\frac { d y } { d x }$$ at $$x = \frac { \pi } { 4 }$$ is:

If $$\theta$$ is angle of intersection between $$y=10-x^{2}$$ and $$y=4+x^{2}$$ then $$|\tan \theta|$$ is-

The function $$f(x)=\sqrt{25-4x^{2}}$$ is increasing in

The function log (log x) increases in 

The function f defined by $$f(x)=(x+2)e^{-x}$$ si

If $$f:R\rightarrow R$$ is the function defined by $$f\left( x \right) =\frac { { e }^{ { x }^{ 2 } }-{ e }^{ -x^{ 2 } } }{ { e }^{ x^{ 2 } }+{ e }^{ { -x }^{ 2 } } } ,$$ then

Let $$f(x)=\left\{\begin{matrix} max \{|x|, x^2\}, & |x|\leq 2\\ 8-2|x|, & 2 < |x|\leq 4\end{matrix}\right.$$
Let S be the set of points in the interval $$(-4, 4)$$ at which f is not differentiable. Then S?