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Lt(x to oo) ((a^((1)/(x))+b^((1)/(x))+c^...

`Lt_(x to oo) ((a^((1)/(x))+b^((1)/(x))+c^((1)/(x)))/(3))^(x)` when a,b,c are non zero positive real numbers)=

A

0

B

`(abc)^(1//3)`

C

abc

D

`abc//3`

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The correct Answer is:
B
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AAKASH SERIES-LIMITS-EXERCISE-II
  1. Lt(x to 0) ((2^(x)+2^(2x)+2^(3x))/(3))^(1//x)=

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  2. Lt(x to oo) ((a(1)^((1)/(x))+a(1)^((1)/(x))+....+a(n)^((1)/(x)))/(n))(...

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  3. Lt(x to oo) ((a^((1)/(x))+b^((1)/(x))+c^((1)/(x)))/(3))^(x) when a,b,c...

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  4. Observe the following lists : The correct match is

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  5. Lt(x to0) ((|x|)/(x)+x+2)=

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  6. Lt(x to0)(sinx^(2))/(|x|)=

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  7. Lt(x to0)(1)/(x)=

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  8. Lt(x to 0) (1)/(2) (sqrt(1-cos2x))/(x)=

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  9. f(x)=(tanx)/(sqrt(1+tan^(2)x)) and f((pi)/(2)-)=a,f((pi)/(2)+)=b then

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  10. underset(x to oo)"Lt" (e^(1//x)-e^(-1//x))/(e^(1//x)+e^(-1//x))=

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  11. Assertion (A) : Lt(x to0) (x)/(1+e^((1)/(x)))=0 Reason(R) : As x to...

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  12. If f: R to R is defined by f(x)==[x-3]+|x-4| for x in R then Lt(x to3...

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  13. Lt(x to 1){1-x+[x-1]+[1-x])=

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  14. If l(1)= Lt(x to2^(+))(x+[x]),l(2)=Lt(x to 2^(-))(2x-[x]) and l(3)=Lt...

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  15. Lt(x to (pi)/(2))[ sinx]=

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  16. If f(x)= {{:(,2x+b,(x lt a)),(,x+d,(x ge a)):}" is such that " underse...

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  17. If f(x)={{:(1 ,if "x is reational"),(-1, if "x is irrational"):}then ...

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  18. f(x)={{:(x ",",if "x is reational"),(-x",", if "x is irrational"):} L...

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  19. If f(x)={{:((sin(1+[x]))/([x]),"for" ,[x] ne 0),(0,"for",[x] =0):} whe...

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  20. If f: R to R is defined by {{:((x-2)/(x^(2)-3x+2),"if" x ne R-{1,2})...

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