If a function $$f(x)$$ is defined as $$f(x)=xx2$$ ,x≠$$00$$, $$x=0$$ then

Correct option is 3f(x) is not continuous at x=0

Questions

$If a function f (x) is defined as f (x) = \{\begin{cases} \frac{x}{\sqrt{x^{2}}}, x \neq 0 \\ 0, x = 0 \end{cases} then$

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f(x) continuous at x=0 but not differentiable at x=0

f(x) is continuous as well as differentiable at x=0

f(x) is not continuous at x=0

f(x) is continuous everywhere

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detailed solution

Correct option is C

fx=xx2 , x≠00 , x=0=x|x|, x≠00, x=0 ∴f(x) is not continuous at x=0=1 , x>0−1 , x<00 , x=0

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If a function f(x) is defined as f(x)=xx2 ,x≠00, x=0 then

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

$If a function f (x) is defined as f (x) = \{\begin{cases} \frac{x}{\sqrt{x^{2}}}, x \neq 0 \\ 0, x = 0 \end{cases} then$