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Fill in the blanks: An example of a fu...

Fill in the blanks:
An example of a function which is continuous everywhere but fails to be differentiable exactly at two points 2 and 3 is …………… .

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Fill in the blanks: If f(x) = |sin x|, then f'(pi/4) is equal to ………...

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  2. Fill in the blanks: Domain of continuity of the function f(x) =|x-1|...

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  3. Fill in the blanks: An example of a function which is continuous eve...

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  4. Fill in the blanks: For the curve sqrtx + sqrty = 1, dy/dx at (1/4, ...

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  5. Fill in the blanks: If f(x) = x^(2//3), then f'(0) is ……… .

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  6. Fill in the blanks: Rolle's Theorem is not applicable to the functio...

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  7. Every continuous function is differentiable.

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  8. True or False : d/(dx) (logx) = 1/x for all x ne 0.

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  9. True or False : d/(dx) (log|x|) = 1/x for all x ne 0

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  10. If f is continuous on its domain D, then |f| is also continuous on D.

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  11. True or False : Rolle's Theorem is applicable to the function f(x) =...

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  12. Verify the truth of Rolle's Theorem for the following functions: f(X...

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  13. True or False : The function f(x) = log x^2 has only one point of di...

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  14. The composition of two continuous function is a continuous function.

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  15. true false: cos|x| is differentiable every where.

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  16. True or False : The function f(x) = {:{(x+a, xge1),(ax^2 +1, x <1):}...

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  17. True or False : The function f(x) = |sinx| is differetiable at all ...

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  18. Find ainR so that f(x) = {:{(x^2, x ge0),(ax,x<0):} is continuous at 0...

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  19. For continuity, at x=a, each of lim(xtoa^(+))f(x) and lim(xtoa^(-))f(x...

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  20. True or False : d/(dx) (log10x) = 1/x for all x >0

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