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Let f (x)= {{:(x [x] , 0 le x lt 2),( (x...

Let `f (x)= {{:(x [x] , 0 le x lt 2),( (x-1), 2 le x le 3):}` where [x]= greatest integer less than or equal to x, then:
The number of values of x for `x in [0,3]` where `f (x)` is non-differentiable is :

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
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VK JAISWAL-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (COMPREHENSION TYPE PROBLEMS)
  1. Consider a function f (x) in [0,2pi] defined as : f(x)=[{:([sinx]+ ...

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  2. Let f (x)= {{:(x [x] , 0 le x lt 2),( (x-1), 2 le x le 3):} where [x]=...

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  3. Let f (x)= {{:(x [x] , 0 le x lt 2),( (x-1), 2 le x le 3):} where [x]=...

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  4. Let f (x)= {{:(x [x] , 0 le x lt 2),( (x-1), 2 le x le 3):} where [x]=...

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  5. Let f :R to R be a continous and differentiable function such that f (...

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  6. Let f :R to R be a continous and differentiable function such that f (...

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  7. Let f :R to R be a continous and differentiable function such that f (...

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  8. f(x)=(cos^2x)/(1+cosx+cos^2x) and g(x)=ktanx+(1-k)sinx-x, where k in R...

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  9. f(x)=(cos^2x)/(1+cosx+cos^2x) and g(x)=ktanx+(1-k)sinx-x, where k in R...

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  10. f (x) = lim (x to oo) (x ^(2) + 2 (x+1)^(2n))/((x+1) ^(2n+1) + x^(2) +...

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  11. f (x) = lim (x to oo) (x ^(2) + 2 (x+1)^(2n))/((x+1) ^(2n+1) + x^(2) +...

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  12. f (x) = lim (x to oo) (x ^(2) + 2 (x+1)^(2n))/((x+1) ^(2n+1) + x^(2) +...

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  13. Let f and g be two differentiable functins such that: f (x)=g '(1) s...

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  14. Let f and g be two differentiable functins such that: f (x)=g '(1) s...

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  15. Let f and g be two differentiable functins such that: f (x)=g '(1) s...

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  16. Suppose a function f(x) satisfies the following conditions f (x+y) =...

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  17. Suppose a function f(x) satisfies the following conditions f (x+y) =...

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  18. Let f (x) be a polynomial satisfying lim (x to oo) (x ^(4) f (x))/( x ...

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  19. Let f (x) be a polynomial satisfying lim (x to oo) (x ^(4) f (x))/( x ...

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  20. Consider f (x) = x ^(ln x), and g (x) = e ^(2) x. Let alpha and beta b...

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