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If f(x)=-sqrt(25-x^(2))", then " underse...

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

A

`(-1)/(sqrt(24))`

B

`(1)/(sqrt(12))`

C

`(1)/(sqrt(24))`

D

`(11)/(sqrt(12))`

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-LIMITS-PRACTICE EXERCISE
  1. If underset(x to o)"Lt" (log(3+x)-log(3-x))/(x)=k then k=

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. The correct match is

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

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

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

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  20. Lt(x to 0) (a cosx+bx sin x-5)/(x^(4)) is finite then a =

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