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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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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Examine the continuity of the function f(x) = {:{(3x-2,xle0),(x+1,x>0)...

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  2. Is the function f(X) = {:{((1-x^n)/(1-x), x ne 1),(n-1,x=1):}, n in N ...

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

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  4. Determine the value of the constant k so that the function f(x) = {:{(...

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  5. Determine the value of the constant k so that the function f(x) = {:{(...

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  6. Determine the value of the constant k so that the function f(x) = {:{(...

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  7. Determine the value of the constant k so that the function f(x) = {:{(...

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  8. Determine the value of the constant k so that the function f(x) = {:{(...

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  9. Determine the value of the constant k so that the function f(x) = {:{(...

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  10. Determine the value of the constant k so that the function f(x) = {:{(...

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  11. Find the values of a so that the function f defined by f(X) = {:{((sin...

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  12. Find the value of a if the function f defined by f(x) = {:{(2x-1, x < ...

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  13. Show that the function f(x) = |x + 1| + | x - 1| is continuous at x = ...

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  14. Consider the functions defined as follows, for x ne 0. In each case, w...

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  15. Consider the functions defined as follows, for x ne 0. In each case, w...

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  16. Find ainR so that f(x) = {:{(x^2, x ge0),(ax,x<0):} is continuous at 0...

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  17. Find k in R if f(x) = {:{((cos^2 x - sin^2 x -1)/(sqrt(x^2+1) - 1), x ...

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  18. Let f(x) = {:{((1-cosax)/(xsinx), x ne 0),(1/2, if x = 0):} If f is co...

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  19. Find the value of the constant k so that function f(x) = {{:((k cos ...

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  20. Examine the following functions for continuity: f(x) = {:{(x^n sin1/...

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