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If f(x) = {{:((x)/(|x| + 2x^2)"," ,x != ...

If `f(x) = {{:((x)/(|x| + 2x^2)"," ,x != 0),(k",", x = 0):}`
Prove that `f(x)` remain discontinous at `x = 0` for any real value of k.

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The correct Answer is:
Discontinuous
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BETTER CHOICE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-ASSIGNMENT (MOST IMPORTANT QUESTIONS FOR PRACTICE)(SECTION II)(SHORT ANSWER TYPE QUESTIONS)
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  3. If f(x) = {{:((x)/(|x| + 2x^2)"," ,x != 0),(k",", x = 0):} Prove tha...

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  6. Test the continuity of the following functions at indicated points : ...

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  10. Find k, so that f(x) = {{:((sin kx)/(x)"," ,x != 0),(4+ x",", x = 0):}...

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  12. For what value of k is the function defined by f(x) = {{:(k(x^2 + 2)...

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  13. Find the value of k so that f(x) is continous at x = 0 f(x) = {{:((1...

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  14. Find the value of k so that f(x) is continouns at x = 0 f(x) = {{:((...

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  16. Determine the constant lambda , so that the function is continuous at ...

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  17. For what value of k is the following function continous at x = 2 ? f...

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  19. Find all the points of discontinuity, where f is defined by f(x) = {...

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