The function \[f(x)={{x}^{2}}\,\,\sin \frac{1}{x},\,x\ne \,0,\,\,f – McqOptions

MCQOPTIONS

1.	The function \[f(x)={{x}^{2}}\,\,\sin \frac{1}{x},\,x\ne \,0,\,\,f(0)\,=0\] at \[x=0\] [MP PET 2003]
A.	Is continuous but not differentiable
B.	Is discontinuous
C.	Is having continuous derivative
D.	Is continuous and differentiable
Answer» E.

Discussion

No Comment Found

Related MCQs

The domain of the derivative of the function \[f(x)=\left\{ \begin{align} & {{\tan }^{-1}}x\ \ \ \ \ ,\ |x|\ \le 1 \\ & \frac{1}{2}(|x|\ -1)\ ,\ |x|\ >1 \\ \end{align} \right.\] is [IIT Screening 2002]
The function \[f(x)=\frac{{{\sec }^{-1}}x}{\sqrt{x-[x]}},\] where [.] denotes the greatest integer less than or equal to x is defined for all x belonging to
The function f satisfies the functional equation \[3f(x)+2f\left( \frac{x+59}{x-1} \right)=10x+30\] for all real \[x\ne 1\]. The value of \[f(7)\] is [Kerala (Engg.) 2005]
If \[f(x)=\frac{x-|x|}{|x|}\], then \[f(-1)=\] [SCRA 1996]
If x is real, then value of the expression \[\frac{{{x}^{2}}+14x+9}{{{x}^{2}}+2x+3}\] lies between [UPSEAT 2002]
If \[f(x)=\left\{ \begin{align} & \,\,\,\,\,\,\,\,\,\,\,\,1,\,\,x
Suppose \[f(x)\] is differentiable at \[x=1\] and \[\underset{h\to 0}{\mathop{\lim }}\,\frac{1}{h}f(1+h)=5\] , then \[f'(1)\] equals [AIEEE 2005]
The function \[f(x)={{x}^{2}}\,\,\sin \frac{1}{x},\,x\ne \,0,\,\,f(0)\,=0\] at \[x=0\] [MP PET 2003]
The domain of the function \[f(x)=\frac{1}{{{\log }_{10}}(1-x)}+\sqrt{x+2}\] is [DCE 2000]
If function \[f(x)=\frac{1}{2}-\tan \left( \frac{\pi x}{2} \right)\]; \[(-1