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If f(x) = {(kx^(2),"if"x le 2),(3,"if" x...

If `f(x) = {(kx^(2),"if"x le 2),(3,"if" x gt 2):}` is continuous at x = 2, then the value of k is

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The correct Answer is:
`K=3/4`
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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(a) (SHORT ANSWER TYPE QUESTIONS)
  1. If f(x) = {(kx^(2),"if"x le 2),(3,"if" x gt 2):} is continuous at x ...

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  2. Check the continuity of the function f given by f(x) = 2x + 3 at x = 1...

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  3. Check the continuity of the following functions : f(x)=x^(2)" at "x=...

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  4. Examine the continuity of the function f(x)=2x^2-1at x = 3.

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  5. Examine the function f(x)=2x^(2)-5 for its continuity at the point x =...

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  6. is f(x)=|x| a continuous function?

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  7. Examine the following functions for continuity : f(x) = x - 5

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  8. Examine the following functions for continuity : f(x)=x^(3)+x^(2)-1

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  9. Examine the following functions for continuity : f(x)=1/(x-5),xne5

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  10. Examine the following functions for continuity : f(x)=(x^(2)-25)/(x+...

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  11. Examine the following functions for continuity: (d) f(x) = |x - 5|.

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  12. Prove that the following functions are continuous at all points of the...

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  13. Prove that the following functions are continuous at all points of the...

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  14. Prove that the following functions are continuous at all points of the...

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  15. Prove that the following functions are continuous at all points of the...

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  16. Discuss the continuity of the following functions a) f(x)=sinx+cosx

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  17. Discuss the continuity of f(x)=sinx-cosx

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  18. Discuss the continuity of f(x)=sinxcosx

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  19. Discuss the continuity of the following functions : f(x)=sinx/cosx.

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  20. Prove that f(x)=|sinx| is continuous at all points of its domain.

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