Question

Let $f\left(x\right)=\sin \frac{1}{x},x\ne 0$.

Then $f\left(x\right)$ can be continuous at $x=0$ for which of the following conditions?

• A. if $f\left(0\right)=1$
• B. if $f\left(0\right)=0$
• C. if $f\left(0\right)=-1$
• D. for no value of $f\left(0\right)$

Answer 1

The correct option is D for no value of $f\left(0\right)$

$\sin \left(1/x\right)$ varies randomly near zero. whatever may be $x$ the value of this lies in $[-1,1]$ .
We cant really assure the value it tends to near zero. the graph of this varies more rapidly.