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Show that the function f(x)={(x^3+3ifxne...

Show that the function `f(x)={(x^3+3ifxne0),(1ifx=0):}` is not continuous at x=0

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V PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Examine whether the function f(x)=x^2 is continuous at x=0

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

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  3. Show that the function f(x)={(x^3+3ifxne0),(1ifx=0):} is not continuou...

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  4. Check the point 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 c...

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

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  7. Discuss the continuity of the function f(x)=x^3+x^2-1

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  8. Discuss the continuity of the function f(x)=1/x,xne0

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  9. Check the continuity of the function f(x)={(x,+,2,if,x,<,0),(-x,+,2,...

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

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  11. Show that every polynomial function is continuous

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  12. Prove that the greatest integer function f : R rarrR given by f(x) =[x...

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  13. Prove that every rational function is continuous.

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  14. Discuss the continuity of sine function.

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

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  16. Prove that the function f(x)=5x-3 is continuous at x=0, at x=-3 and at...

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

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  18. Examine the following functions for continuity f(x)=1/(x-5)

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  19. Prove that the function f(x)=x^n is continuous at x=n, where n is a p...

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  20. Is the function f defined by f(x)={(x","ifxle1),(5"," ifx>1):} continu...

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