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Discuss the continuity and differenti...

Discuss the continuity and differentiability of `f(x)={(x-c)cos(1/(x-c)),\ \ \ x!=c0,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=c`

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RD SHARMA ENGLISH-DIFFERENTIABILITY-All Questions
  1. Discuss the continuity and differentiability of f(x)=|log|x|| .

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  2. Discuss the continuity and differentiability of f(x)=e^(|x|) .

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  3. Discuss the continuity and differentiability of f(x)={(x-c)cos(1/(x...

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  4. Is |sinx| differentiable? What about cos|x|?

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  5. Define differentiability of a function at a point.

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  6. Is every differentiable function continuous?

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  7. Is every continuous function differentiable?

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  8. Give an example of a function which is continuous but not different...

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  9. If f(x) is differentiable at x=c , then write the value of (lim)(x-...

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  10. If f(x)=|x-2| write whether f\ '\ (2) exists or not.

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  11. Write the points where f\ (x)=|(log)e x| is not differentiable.

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  12. Write the points of non-differentiability of f(x)=|log|x|| .

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  13. Write the derivative of f\ (x)=|x|^3 at x=0 .

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  14. Write the number of points where f(x)=|x|+|x-1| is continuous but n...

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  15. If (lim)(x->c)(f(x)-f(c))/(x-c) exists finitely, write the value of...

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  16. Write the value of the derivative of f(x)=|x-1|+|x-3| at x=2 .

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  17. If f(x)=sqrt(x^2+9) , write the value of (lim)(x->4)(f(x)-f(4))/(x-4) ...

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  18. Let f(x)=|x| and g(x)=|x^3| , then (a).f(x) and g(x) both are continuo...

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  19. The function f(x)=sin^(-1)(cosx) is discontinuous at x=0 (b) continuou...

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  20. The set of points where the function f(x)=x|x| is differentiable i...

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