Embibe Experts Solutions for Chapter: Continuity, Exercise 1: MHT-CET 2017

If the function $f\left(x\right)=\left\{\begin{array}{ll}\frac{1-\sin 2x+\cos 2x}{1+\sin 2x+\cos 2x};& x\ne \frac{\pi }{2}\\ k;& x=\frac{\pi }{2}\end{array}\right.$ is continuous at $x=\frac{\pi }{2},$ then $k=$

If $f\left(x\right)=\left\{\begin{array}{l}6\beta -3\alpha x, \text{if} -4\le x<-2\\ 4x+1, \text{if} -2\le x\le 2\end{array}\right.$ is continuous on $[-4,2],$ then $\alpha +\beta =$

If the function $f\left(x\right)=\left\{\begin{array}{cc}\frac{\left(e^{kx}-1\right)\tan kx}{4x^2},& x\ne 0\\ 16,& x=0\end{array}\right.$ is continuous at $x=0$, then $k$ = ….

If function $f\left(x\right)=\left\{\begin{array}{l}x-\frac{\left|x\right|}{x}, x<0\\ 1, x=0\\ x+\frac{\left|x\right|}{x},x>0\end{array}\right.$ , then

If $f\left(x\right)=x^2+\alpha$ for $x\ge 0 \& f\left(x\right)=2\sqrt{x^2+1}+\beta$ for $x<0$ is continuous at $x=0$ and $f\left(\frac{1}{2}\right)=2$ then ${\alpha }^2+{\beta }^2$ is

If $f\left(x\right)=\frac{e^{x^2}-\cos x}{x^2},$ for $x\ne 0$ is continuous at $x=0$ , then value of $f\left(0\right)$ is

If $f\left(x\right)=\left\{\begin{array}{ccc}\log {\left({\sec }^{2}x\right)}^{{\cot }^{2}x}& \mathrm{f}\mathrm{o}\mathrm{r}& x\ne 0\\ K& \mathrm{f}\mathrm{o}\mathrm{r}& x=0\end{array}\right.$ is continuous at $x=0$ then $K$ is

If $f\left(x\right) = \left\{\begin{array}{ccc}x& \text{for}& x\le 0\\ 0& \text{for}& x>0\end{array}\right.$ then $f\left(x\right)$ at $x=0$ is