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For what value of k is the function defi...

For what value of `k` is the function defined by
`f(x) = {{:(k(x^2 + 2)"," ,"if" x lt 0),(3x + 1",", "if "x gt 0):}` continous at `x = 0` ?

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The correct Answer is:
`k = 1/2`
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BETTER CHOICE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-ASSIGNMENT (MOST IMPORTANT QUESTIONS FOR PRACTICE)(SECTION II)(SHORT ANSWER TYPE QUESTIONS)
  1. Examine the continuity of f(x) = {{:((x)/(|x| )"," ,"if " x != 0),(0",...

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  2. If f(x) = {{:((x)/(|x| + 2x^2)"," ,x != 0),(k",", x = 0):} Prove tha...

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  3. Discuss the continuity of the function defined by f(x) = {{:((sin 3x...

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  4. Discuss the continuity of the function defined by f(x) = {{:((tan 2x...

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

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

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

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  8. Determine k, so that f(x) = {{:((x^2 - 36)/(x - 6)"," ,"if " x != 6),(...

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

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  10. Determine k, if the following function is continuous at x = 0 f(x) =...

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

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

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

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  14. Determine the constant k so that the function f(x) = {{:(3k - 2x"," ...

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

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

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

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

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

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  20. Discuss the continuity of the function f(x) at x = 1/2 where f(x) = ...

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