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If f(x) is differentiable at x=c , then ...

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

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If f(x) is differentiable at `x=c`,
then the value of `lim_(x->c)f(x)` will be
`=f(c)`
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RD SHARMA-DIFFERENTIABILITY-Solved Examples And Exercises
  1. Is every continuous function differentiable?

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. If f(x)={(|x+2|)/(tan^(-1)(x+2)),\ \ \ x!=-2 2,\ \ \ \ \ \ \ \ \ \ \ \...

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  16. Let f(x)=|x| . Then, for all x f is continuous (b) f is differentiabl...

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  17. The function f(x)=e^(|x|) is (a) Continuous everywhere but not differ...

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  18. The function f(x)=|cosx| is (a) everywhere continuous and differe...

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  19. If f(x)=sqrt(1-sqrt(1-x^2)) , then f(x) is (a) continuous on [-1, 1...

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  20. If f(x)=a|sinx|+b\ e^(|x|)+c\ |x|^3 and if f(x) is differentiable at x...

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