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let alpha(a) and beta(a) be the roots of...

let `alpha(a)` and `beta(a)` be the roots of the equation `((1+a)^(1/3)-1)x^2 +((1+a)^(1/2)-1)x+((1+a)^(1/6)-1)=0` where `agt-1` then, `lim_(a->0^+)alpha(a)` and `lim_(a->0^+)beta(a)`

A

`-5/2` and 1

B

`-1/2` and -1

C

`-7/2` and 2

D

`-9/2` and 3

Text Solution

Verified by Experts

The correct Answer is:
C
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ARIHANT MATHS-LIMITS-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. Let m and n be two positive integers greater than 1.If lim(alpha->0) (...

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  3. Let f: RvecR be a continuous odd function, which vanishes exactly at o...

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  4. The largets value of non negative integer for which lim(x->1){(-a x+si...

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  5. Let L=("lim")(xvec0)(a-sqrt(a^2-x^2)-(x^2)/4)/(x^4),a > 0. IfLi sfin i...

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  6. The lim(xto(pi)/2)(cot x-cosx)/((pi-2x)^(3)) equals

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  7. Let p=lim(x->0^+)(1+tan^2 sqrt(x))^(1/(2x)) then log p is equal to

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  8. lim(n -> oo) (((n+1)(n+2)(n+3).......3n) / n^(2n))^(1/n)is equal to

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  9. lim(xto0)(sin(picos^(2)x))/(x^(2)) is equal to

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  10. lim(xto0)((1-cosx)(3+cosx))/(x tan 4x) is equal to

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  11. If lim(xtooo)((x^(2)+x+1)/(x+1)-ax-b)=4, then

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  12. let alpha(a) and beta(a) be the roots of the equation ((1+a)^(1/3)-1)x...

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  13. If ("lim")(xvec0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b >0,s mftheta in ...

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  14. For xgt0, lim(xto0) {(sinx)^(1//x)+((1)/(x))^sinx}, is

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  15. underset(h to 0)lim (f(2h+2+h^(2)))/(f(h-h^(2)+1)-f(1))"given that "f'...

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  16. lim(x->0) (sin(nx)((a-n)nx – tanx))/x^2= 0, when n is a non-zero posit...

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  17. The integer n for which lim(x rarr 0) ((cos x-1) ( cos x - e^x))/x^n i...

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  18. Let f:RtoR be such that f(1)=3 andf'(1)=6. Then lim(xto0)[(f(1+x))/(f(...

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  19. For x epsilonR, lim(xto oo)((x-3)/(x+2))^(x) is equal to

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