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Prove that f(x)=|sinx| is continuous at ...

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

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(a) (SHORT ANSWER TYPE QUESTIONS)
  1. Discuss the continuity of f(x)=sinxcosx

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

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

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  4. Examine if sin|x| is a continuous function.

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  5. Is the function defined by f(x)=x^2-sinx+5continuous at x=pi?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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