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If G(x)=-sqrt(25-x^2),then lim(x to 1) (...

If `G(x)=-sqrt(25-x^2)`,then `lim_(x to 1) (G(x)-G(1))/(x-1)` is
(a)`1/(24)`
(b) `1/5`
(c) `-sqrt(24)`
(d) none of these

A

`(1)/(4sqrt(6))`

B

`(1)/(2sqrt(6))`

C

`(1)/(sqrt(6))`

D

`-(1)/(2sqrt(6))`

Text Solution

Verified by Experts

The correct Answer is:
B
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ICSE-LIMITS AND DERIVATIVES -Multiple Choice Questions
  1. If G(x)=-sqrt(25-x^2),then lim(x to 1) (G(x)-G(1))/(x-1) is (a)1/(24...

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  2. Lt(xto0)(sqrt(1+x)-1)/(x) is equal to (i) 0 (ii) 1 (iii) 1/2 ...

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  3. Lt(xto0)(x)/(sin3x) is equal to (i) 3 (ii) 1/3 (iii) 0 (iv) 1

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  4. Lt(xto0)(sqrt(4+x)-2)/(sinx) is equal to (i) 4 (ii) 1 (iii) 1/4...

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  5. If Lt(x to a)(x^(9)-a^(9))/(x-a)=Lt(xto5)(x+4) then all possible value...

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  6. Let f(x)={:{(x+2",",xle-1),(cx^(2)",",xgt-1):} If Lt(xto-1) f(x) exist...

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  7. lim{x\rightarrow 0}(1-cos2x)/(sin^(2)2x) is equal to

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  8. Lt(x to0)(tan3x-2x)/(3x-sin^(2)x) is equal to

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  9. lim{x\rightarrow 0}(1-cosmx)/(1-cos nx) is equal to

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  10. lim{x\rightarrow 0}(cosx-cos3x)/(x(sin 3x-sinx)) is equal to

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  11. Lt(xto0)((1-cos2x)sin5x)/(x^(2)sin3x) is equal to (i) (6)/(5) (ii...

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  12. If Lim(x to 0) k . cosec x=Lim(x to 0)x cosec kx, then k is (i) -1,1...

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  13. Lt(x to pi)(sinx)/(x-pi) is equal to

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  14. Lt(xto1)(sinpix)/(x-1) is equal to

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  15. Lt(x to (pi)/(2))(2x-pi)/(cos x) is equal to

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  16. Lt(x to (pi)/(2))(pi/2-x)tan x is equal to (i) 1 (ii) -1 (iii) (pi)...

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  17. (lim)(x->pi/2)(tan2x)/(x-pi/2)

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  18. Lt(x to 0)(e^(x)+sinx-1)/(3x) is equal to (i) 1/3 (ii) -1/3 (iii) 2/3...

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  19. lim(x to 2)(log(x-1))/(x-2) is equal to

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  20. lim(x to 0)(3^(2x)-2^(3x))/(x) is equal to

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  21. Lt(x to 0)(|x|)/(x) is equal to (i) 1 (ii) -1 (iii) 0 (iv) does not e...

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