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Show that f(x)= {(x^(3)+3",",x ne0),(1",...

Show that `f(x)= {(x^(3)+3",",x ne0),(1",",x=0):}` is a discontinuous function at x= 0.

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KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-Textbook Illustrations for Practice Work
  1. Prove that the function f(x)= x^(2) is continuous at x=0.

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  2. Discuss the continuity of the function f given by f(x)= |x| " at " x=0...

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  3. Show that f(x)= {(x^(3)+3",",x ne0),(1",",x=0):} is a discontinuous fu...

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  4. Check the points where the constant function f(x)= k is continuous

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  5. Prove that the identity function on real numbers given by f(x)=x is co...

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  6. Is the function defined by f(x)= |x|, a continuous function

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  7. Discuss the continuity of the function f given by f(x)= x^(3) + x^(2)-...

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  8. Discuss the continuity of the function f defined by f(x)= (1)/(x), x n...

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  9. Discuss the continuity of the function f defined by f(x)= {(x+2",","if...

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  10. Find all the points of discontinuity of the function f defined by f(x)...

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  11. Discuss the continuity of the function defined by f(x) = {(x+2",","if ...

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  12. Discuss the continuity of the function f given by f(x)= {(x",","if " x...

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  13. Show that every polynomial function is continuous.

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  14. Find all the points of discontinuity of the greatest integer function ...

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  15. Prove that every rational function is continuous

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  16. Discuss the continuity of sine function

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  17. Prove that the function defined by f(x)= tan x is a continuous functio...

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  18. Show that the function defined by f(x)= sin (x^(2)) is a continuous fu...

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  19. Show that the function f defined by f(x)= |1-x + |x|| where x is any r...

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  20. Find the derivative of the function given by f(x)= sin x^(2)

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