Continuity of a Function

Q. Which of the following is not continuous for all x?

1. 
2. 
3. 
4. 

Q. The function $f\left(x\right)=\frac{log(1+ax)-log(1-bx)}{x}$ is not defined at x-0 . The value which should be assigned to f at x = 0 so that it is continuos at x=0 , is

1. a-b
2. a+b
3. loga+logb
4. log a-log b

Q. Let f(x) = $\{\begin{array}{cc}\frac{x^3+x^2-16x+20}{(x-2{)}^2},& ifx\ne 2\\ k,& ifx=2\end{array}.$ if f(x) be continuous for all x, then k =

1. 7
2. -7
3. None of these
4. 

Q. $Letf\left(x\right)=\{\begin{array}{cc}{(1+|sinx|)}^{\frac{a}{|sinx|}},& \frac{-x}{6}<x<0\\ b,& x=0\\ e^{tan2x/tan3x},& 0<x<\frac{-\pi }{6}\end{array}$ then the value of a and b if f is continuous at x=0, are respectively

1. 
2. 
3. None of these
4. 

Q. The function $f\left(x\right)-p[x+1]+q[x-1]$, where is the greatest integer function is continuous at x =1, if

1. p-q=0
2. p+q=0
3. p=0
4. q=0

Q. The value of p for which the function $f\left(x\right)=\frac{(4^x-1{)}^3}{sin\left(\frac{x}{p}\right)ln(1+\frac{x^2}{3})},x\ne 0=12(ln4{)}^3,x=0$ may be continuous at x = 0 is

1. 3
2. 4
3. 2
4. 1

Q. The value of f(0), so that the function $f\left(x\right)=\frac{1-cos(1-cosx)}{x^4}$ is continuous everywhere is

1. 
2. 
3. 
4. 

Q. If $f\left(x\right)=\{\begin{array}{cc}xsinx,& when0<x\le \frac{\pi }{2}\\ \frac{\pi }{2}sin(\pi +x),& when\frac{\pi }{2}<x<\pi \end{array},then$

1. f(x) is continuous at x = 0
2. f(x) is discontinuous at x = π / 2
3. f(x) is continuous at x = π / 2
4. None of these

Q. If the function $f\left(x\right)=\begin{array}{cc}(1+|sinx|{)}^{\frac{a}{|sinx|}},& -\frac{\pi }{6}<x<0\\ b,& x=0\\ e^{\frac{tan2x}{tan3x}},& 0<x<\frac{\pi }{6}\end{array}$, is continuous at x = 0, then

1. 
2. 
3. 
4. 

Q.

The value of f(0) so that the function $f\left(x\right)=\frac{1-cos(1-cosx)}{x^4}$ is continuous everywhere is

1. none of these

2. $\frac{1}{8}$

3. $\frac{1}{4}$

4. $\frac{1}{2}$