The function $f(x) = |x|$ at $x = 0$ is

Let $a_1, a_2, \ldots, a_{100}$ be non-zero real numbers such that $a_1+a_2+\ldots+a_{100}=0$. Then,

Let $f(x) = \begin{cases} e^{x-1}; x < 0 \\ x^2-5x+6; x \ge 0 \end{cases}$ and $g(x) = f(|x|) + |f(x)|$. If the number of points where $g$ is not continuous and is not differentiable are $\alpha$ and $\beta$ respectively,then $\alpha + \beta$ is equal to ————

If $f(x)=\sin \left(\cos ^{-1}\left(\frac{1-2^{2 x}}{1+2^{2 x}}\right)\right)$ and its first derivative with respect to $x$ is $-\frac{ b }{ a } \log _{ e } 2$ when $x =1,$ where $a$ and $b$ are integers,then the minimum value of $\left| a ^{2}- b ^{2}\right|$ is.........

Let $f(x)$ be a differentiable function,$f^{\prime}(x) > f(x)$ and $f(0) = 0$. Then

The function $f(x) = \sqrt{1 - \sqrt{1 - x^2}}$