Let $f:(0, \infty) \rightarrow(0, \infty)$ be a dif ferentiable function such that $f(1)=e$ and $\lim _{t \rightarrow x} \frac{t^2 f^2(x)-x^2 f^2(t)}{t-x}=0$ If $f(x)=1$, then $x$...

Let $K$ be the set of all real values of $x$ where the function $f(x)=\sin |x|-|x|+2(x-\pi)$ is not differentiable. Then the set K is equal...

Let $S$ be the set of points where the function, $f(x)=|2-|x-3| \|, x \in R$, is not differentiable. Then $\sum_{x \in S} f(f(x))$ is equal...

If the function $f(x)=\left\{\begin{array}{ll}a|\pi-x|+1, & x \leq 5 \\ b|x-\pi|+3, & x>5\end{array}\right.$ is continuous at $x=5$, then the value of $a-b$ is :

If the function $\mathrm{f}(\mathrm{x})=\left\{\begin{array}{cc}\frac{1}{x} \log _e\left(\frac{1+\frac{a}{x}}{1-\frac{x}{b}}\right) & , x<0 \\ k & , x=0 \\ \frac{\cos ^2 x-\sin ^2 x-1}{\sqrt{x^2+1}-1} & , x>0\end{array}\right.$
Is continuous...

Let $f:(-1,1) \rightarrow R$ be a function defined by $f(x)=\max \left\{-|x|,-\sqrt{1-x^2}\right\}$. If $K$ be the set of all points at which $f$ is not differentiable,...

The function $f(x)=\left|x^2-2 x-3\right| . e^{\left|9 x^2-12 x+4\right|}$ is not differentiable at exactly:

Let $a, b \in R, b \neq 0$, Define a function $...

Let $f: R \rightarrow R$ be a function defined as $$ f(x)=\left\{\begin{array}{rrr} 5, & \text { if } & x \leq 1 \\ a+b x,...

Let $[t]$ denote the greatest integer less than or equal to $t$. Let $f(x)=x-[x], g(x)=1-x+[x]$, and $h(x)= \min \{f(x), g(x)\}, x \in[-2,2]$. Then $h$ is...