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lim(x -> oo) ((x-3)/(x+2))^x is equal to...

`lim_(x -> oo) ((x-3)/(x+2))^x` is equal to

A

e

B

`e^(-1)`

C

`e^(-5)`

D

`e^(5)`

Text Solution

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The correct Answer is:
C
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AAKASH INSTITUTE-CONTINUITY AND DIFFERENTIABILITY-Section -B
  1. lim(x->oo)(sqrt(x+sqrt(x))-sqrt(x))equals

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  2. lim(x->0)(1/(x^2)-1/(tan^2x))

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  3. lim(x -> oo) ((x-3)/(x+2))^x is equal to

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  4. lim(x to 0){(1+tanx)/(1+sinx)}^("cosec x") is equal to

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  5. lim(x->0)((4^x+9^x)/2)^(1/x)

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  6. If underset (xrarr0)"lim"(cos+asinbx)^(x/y)=e^(2) then the values of a...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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