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  • The value of k which makes <img alt="\mathrm{f(x)=\left\{\begin{array}{cc}\sin (1 / x), & x \neq 0 \\ k & , x=0\end{array}\right.}" src="https://entrancecorner.oncodecogs.com/gif.latex

The value of k which makes \mathrm{f(x)=\left\{\begin{array}{cc}\sin (1 / x), & x \neq 0 \\ k & , x=0\end{array}\right.}

continuous at x=0 is.

Option: 1

8


Option: 2

1


Option: 3

-1


Option: 4

None of these.


Answers (1)

best_answer

We have \mathrm{\lim _{x \rightarrow 0} f(x)=\lim _{x \rightarrow 0} \sin \frac{1}{x}=} An oscillating number which oscillates between -1 and 1 .
Hence, \mathrm{\lim _{x \rightarrow 0} f(x)} does not exist. Consequently f(x) cannot be continuous at x=0 for any value of k.

Posted by

jitender.kumar

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