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limx->(2^+) ([x]^3/3-[x/3]^3) is...

`lim_x->(2^+) ([x]^3/3-[x/3]^3)` is

A

0

B

`64/27`

C

`8/3`

D

None of these

Text Solution

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The correct Answer is:
C
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AAKASH INSTITUTE-CONTINUITY AND DIFFERENTIABILITY-Section -B
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  2. If underset (xrarr0)"lim"(cos+asinbx)^(x/y)=e^(2) then the values of a...

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  3. lim(x to 0) (sqrt(1- cos 2x))/(sqrt2x) =

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  4. limx->(2^+) ([x]^3/3-[x/3]^3) is

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  5. The value of f(0) so that f(x) = ((4x^(x)-1)^(3))/(sin(x/4)log(1+(x^...

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  6. If f(x)= {:{((x^(2) + 3x+p)/(2(x^(2)-1)) , xne 1),(5/4, x = 1):} is co...

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  7. In order that the function f(x)=(x+1)^(cotx) is continuous at x = 0, f...

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  8. The number of points at which the function f(x) = 1/ (log |2x|) is di...

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  9. If f(x)={:{(xe^(-(1/(|x|) + 1/x)), x ne 0),(0 , x =0 ):} then f(x) is

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  10. The set of points where f(x)=x/(1+|x|) is differentiable is

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  11. The function |x^2 - 3x+2| + cos |x| is not differentiableat x=

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  12. At x = 0 , the function y = e^(-|x|) is

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  13. Let f(x) = lambda + mu|x|+nu|x|^2, where lambda,mu, nu in R, then f'(0...

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  14. If {x} denotes the fractional part of x, then underset(x to 0)(lim) ({...

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  15. Let f(x) = [x] , g(x)= |x| and f{g(x)} = h(x) ,where [.] is the gre...

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  16. A function f is defined by f(x^(2) ) = x^(3) AA x gt 0 then f(4) equ...

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  17. If 3sin(x y)+4cos(x y)=5,t h e n(dy)/(dx)= -y/x (b) (3sin(x y)+4c...

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  18. Let f(x) = max { 4, 1+x^(2) ,x^(2) -1} AA x in R Total numbner of poi...

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  19. Let g(x) be the inverse of the function f(x) ,and f'(x) 1/(1+ x^(3)) ...

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  20. If f is a real- valued differentiable function satisfying |f(x) - f(y)...

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