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Consider a function f (x) in [0,2pi] def...

Consider a function `f (x)` in `[0,2pi]` defined as :
` f(x)=[{:([sinx]+ [cos x],,, 0 le x le pi),( [sin x] -[cos x],,, pi lt x le 2pi):}`
where {.} denotes greatest integer function then.
`lim _(x to ((3pi)/(2))^+), f (x)` equals

A

0

B

1

C

`-1`

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
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VIKAS GUPTA (BLACK BOOK)-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (COMPREHENSION TYPE PROBLEMS)
  1. Consider a function defined in [-2,2] f (x)={{:({x}, -2 le x lt -1),...

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  2. Consider a function f (x) in [0,2pi] defined as : f(x)=[{:([sinx]+ ...

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  3. Consider a function f (x) in [0,2pi] defined as : f(x)=[{:([sinx]+ ...

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

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

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

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

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

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

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  11. Let f (x) (cos ^(2) x)/(1+ cos +cos ^(2)x )and g (x) lamda tan x+1(1-l...

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

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

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

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

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

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

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

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