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Let f (x) = lim (n to oo) n ^(2) tan (ln...

Let `f (x) = lim _(n to oo) n ^(2) tan (ln(sec""(x)/(n )))and g (x) = min (f(x), {x}}`
(where {.} denotes fractional part function)
Left derivative of `phi(x) =e ^(sqrt(2f (x)))at x =0` is:

A

0

B

1

C

`-1`

D

Does not exist

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. Let f (x) = lim (n to oo) n ^(2) tan (ln(sec""(x)/(n )))and g (x) = mi...

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  2. Let f (x) = lim (n to oo) n ^(2) tan (ln(sec""(x)/(n )))and g (x) = mi...

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  3. Let f (x) and g (x) be two differentiable functions, defined as: f (...

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  4. Let f (x) and g (x) be two differentiable functions, defined as: f (...

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  5. Define: f (x) =|x^(2)-4x +3| ln x+2 (x-2)^(1//3) , x gt 0 h (x)= {{:...

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  6. Define: f (x) =|x^(2)-4x +3| ln x+2 (x-2)^(1//3) , x gt 0 h (x)= {{...

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  7. Consider a function defined in [-2,2] f (x)={{:({x}, -2 lle x lt -1)...

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  8. Consider a function defined in [-2,2] f (x)={{:({x}, -2 le x lt -1),...

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

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

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

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

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

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

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

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

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

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

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

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

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