If the function $g(x)=\begin{cases} K \sqrt{x+1} &, 0 \leq x \leq 3 \\ mx+2 &, 3 < x \leq 5 \end{cases}$ is differentiable, then $K+m=$

If $f(x) = \begin{cases} \frac{x \ln(\cos x)}{\ln(1 + x^2)} & x \neq 0 \\ 0 & x = 0 \end{cases}$,then:

Let $f: R \rightarrow R$ be a function defined by $f(x) = \max \{x, x^2\}$. Let $S$ denote the set of all points in $R$ where $f$ is not differentiable. Then $S$ is:

The points at which the function $f(x) = |x - 0.5| + |x - 1| + \tan x$ does not have a derivative in the interval $(0, 2)$ are:

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

If the function $g(x) = \begin{cases} ae^x, & x \le 0 \\ b\cos x + x, & x > 0 \end{cases}$ is differentiable,then the value of $a^2 + b^2$ is