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If l(1)= Lt(x to2^(+))(x+[x]),l(2)=Lt(x...

If `l_(1)= Lt_(x to2^(+))(x+[x]),l_(2)=Lt_(x to 2^(-))(2x-[x]) and l_(3)=Lt_(x to pi//2)(cosx)/((x-(pi)/(2)))` then

A

`l_(1) lt l_(2) lt l_(3)`

B

`l_(2) lt l_(3) lt l_(1)`

C

`l_(3) lt l_(2) lt l_(1)`

D

`l_(1) lt l_(3) lt l_(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-LIMITS-EXERCISE-II
  1. Lt(x to 0) (1)/(2) (sqrt(1-cos2x))/(x)=

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

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

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

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

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

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

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

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

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

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

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

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  14. Lt(x to0)x^(x)=

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  15. Lt(x to 0)((1)/(x))^(tanx)=

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  16. Lt(x to 0) log(x) sin x=

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  17. If g(x)=(x)/([x]) for x>2, then lim(xrarr2)(g(x)-g(2))/(x-2) is equal ...

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  18. lim(x to pi/2) ((2 x - pi)/(cos X)) =

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  19. underset(x to 0)"Lt" (sqrt(1+x^(2))-sqrt(1-x+x^(2)))/(3^(x)-1)=

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  20. If f(x)=x Tan^(-1) x" then "underset(x to 1)"Lt" (f(x-f(1))/(x-1)=

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