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Show that the function f(x)defined as f(...

Show that the function `f(x)`defined as `f(x) = xcos(1/x),x!=0; 0,x=0`is continuous at `x=0` but not differentiable at x=0..

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(a) (SHORT ANSWER TYPE QUESTIONS)
  1. Discuss the continuity of the function f defined by f(x)=1/x , x!=0.

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

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

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

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

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

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

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

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

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  10. Discuss the continuity of the function f, where f is defined byf(x)={...

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  11. Discuss the continuity of the function : f(x)={{:(x", "0lexlt1/2),(...

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  12. Discuss the continuity of the function : f(x)={{:((1-cosx)/x^(2)", "...

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  13. Show that the function f(x)defined as f(x) = xcos(1/x),x!=0; 0,x=0is c...

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  14. Show that the following functions are continuous at x = 0 : f(x)={{:...

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  15. Test the continuity of the function f (x) : f(x)={{:(x^(2)sin.(1)/(...

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  16. f(x)={{:(cosx",","when",x ge0, ),(-cosx",", "when", x lt0):} is discon...

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  17. Examine the continuity of the function f(x) at x = 0. f(x)={{:(sinx/...

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  18. Examine the continuity of the funcation f(x)={{: ((|sinx|)/x",", xne...

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  19. Examine the continuity of the function f(x) at x = 0. f(x)={{:((tan2...

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  20. Discuss the continuity of the cosine, cosecant, secant and cotangen...

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