Continuity and ...

If $$u=f(x,y)$$ is a differentiable function of $$x$$ and $$y$$, where $$x$$ and $$y$$ are differentiable functions of $$t$$ then:

The set of points, where the function $$f(x) = x|x|$$, is differentiable, is given by

The function $$\displaystyle f(x) = (x^2 - 1) |x^2 - 3x + 2| + cos (|x|)$$, is not differentiable at x=

Let $$f:\left[ {0,2} \right] \to R$$ a function which is continuous on $$\left[ {0,2} \right]$$ and is differentiable on $$\left( {0,2} \right)$$ with $$f\left( 0 \right) = 1$$. Let $$F\left( x \right) = \int\limits_0^{{x^2}} {f\left( {\sqrt t } \right)} dt,$$ for $$x \in \left[ {0,2} \right]$$, if $$F'\left( x \right) = f'\left( x \right),\forall x \in \left( {0,2} \right),$$ then $$F(2)$$ equals to 

If $$\int_{1}^{3} F'(x)dx=-12$$ and $$\int_{1}^{3} x^{3} F' '(x) dx=40$$, then the correct expression(s) is/are

Which of the following function is differentiable at x=0

If $$f : R \rightarrow R$$ is defined by
$$f(x) = \left \{\begin{matrix} \dfrac{x + 2}{x^2 + 3x + 2} & if & x \in R - \{-1, -1\} \\ -1 & if & x = -2 \\ 0 & if  &x = -1\end{matrix} \right.$$ then $$f(x)$$ continuous on the set 

If $$x=a\cos^{3}\theta, y=a\sin^{3}\theta$$, then $$1+ {(\dfrac {dy}{dx})}^{2}$$ is

If $$ f\left( x+y \right) =f\left( x \right) +f\left( y \right)$$ then $$ f\left( x \right)$$ may be

The function $$f\left( x \right) = \,{\sin ^{ - 1}}\left( {\cos \,x} \right)\,is\,: - $$