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Show that the function defined by g(x)=x...

Show that the function defined by `g(x)=x-[x]` is discontinuous at all integral points which [x] denotes the greatest integer function.

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(a) (SHORT ANSWER TYPE QUESTIONS)
  1. Is the function defined by f(x)=x^2-sinx+5continuous at x=pi?

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  2. Show that f(x)=x-|x|,x inR is continuous at x = 0.

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  3. Show that the function defined by g(x)=x-[x] is discontinuous at all i...

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

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  5. Find all points of discontinuity of f, where f is defined byf(x)={(x^...

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  6. Find all points of discontinuity of f, where f is defined byf(x)={(2x...

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  7. Find all points of discontinuity of f, where f is defined byf(x)={(|x...

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  8. Find all points of discontinuity of f, where f is defined byf(x)={x/(...

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  9. Is the function defined by f(x)={x+5, ifxlt=1x-5, ifx >1 a continuous...

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  10. Is the function f defined by f(x)={{:(x, if x le 1),(5, if x gt 1):...

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  11. Show that the function f given by f(x)={x^3+3if""""x!=0 1if""""x=0 is ...

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  12. Discuss the continuity of the function f defined by f(x)=1/x , x!=0.

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  13. Discuss the continuity of the function : f(x)={{:(x",if "xge0),(x^(2...

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  14. Discuss the continuity of the function defined byf(x)={x+2, ifx<0-x+2,...

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  15. Examine the continuity of the function : f(x)={{:(x+1" , "xle2),(2x-...

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  16. f(x)={{:((x^(2)-25)/(x-5)",","when",x ne 5),( 10",", "when",x=5):} is ...

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  17. Discuss the continuity of the function : f(x)={{:((|x-2|)/(x-2)", "x...

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  18. Discuss the continuity of the function : f(x)={{:((|x-2|)/(2-x)", "x...

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  19. Discuss the continuity of the function : f(x)={{:((|x-a|)/(x-a)",whe...

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  20. Discuss the continuity of the function f, where f is defined by f(x){{...

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