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Statement-I : If Lt(x to 0)f(x) exists, ...

Statement-I : If `Lt_(x to 0)f(x)` exists, then `Lt_(x to a)f(x)=Lt_(x to0)f(a+x)=Lt_(x to 0) f(a-x)`
Statement-II : `Lt_(x to (pi)/(2))((cotx)/(x-(pi)/(2)))=1` which one of the following is correct

A

only I

B

only II

C

both I & II

D

Neither I nor II

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The correct Answer is:
A
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AAKASH SERIES-LIMITS-PRACTICE EXERCISE
  1. Evaluate Lt(x to 0) (e^(x) -1)/(sqrt(1 + x) - 1)

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  2. If underset(x to o)"Lt" (log(3+x)-log(3-x))/(x)=k then k=

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  3. Statement-I : If Lt(x to 0)f(x) exists, then Lt(x to a)f(x)=Lt(x to0)f...

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  4. If f(x)=-sqrt(25-x^(2))", then " underset(x to 1)"Lt" (f(x)-f(1))/(x-1...

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  5. f(x)=3x^(2)-4x+5,Lt(x to 1) (f(x)-f(1))/(x-1)=

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  6. Lt(x to 0)(e^(alphax)-e^(betax))/(sin alphax- sin betax)=

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  7. Lt(x to pi//2)(a^(cotx)-a^(cosx))/(cotx-cosx)=

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  8. Lt(x to 0)((1+x^(2))^(1//3)-(1-2x)^(1//4))/(x+x^(2))

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  9. Let f(a)=g(a)=k and the their nth derivatives f^(n)(a),g^(n)(a) exixst...

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  10. Lim(x to 0)(x)/(""^(3)sqrt(x^(2)+3x+8)-""^(3) sqrt(x^(2)-5x+8))=

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  11. Lt(x to 0) (tan^(4)x-sin^(4)x)/(x^(6))=

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  12. The arrangement of the following limit values in the ascending order C...

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  13. Lt(x to 0) {"cosec"^(3)x. cotx-2cot^(3)x."cosec"x+(cot^(4))/(secx)}=

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  14. If 'alpha' is a repeated root of ax^(2)+bx+c=0 then Lt(x to alpha)(tan...

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  15. Lt(x to 0) (1)/(x) sin^(-1)((2x)/(1+x^(2)))=

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  16. Lt(x to 0)(1-cos(x^(0)))/(x^(2))=

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  17. The correct match is

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  18. Lt(x to 0) (sin(x^(0)))/(tanx^(0))=

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  19. Lt(x to 0) ((cosx)^((1)/(2))-(cosx)^((1)/(3)))/(sin^(2)x)=

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  20. If Lim(x to 0) (sin2x+asinx)/(x^(3))=b where a,b in R then (a,b)=

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