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Let `alpha(a) and beta(a)` be the roots of the equation `{(a+1)^(1//3)-1}x^(2)+(sqrt(1+a)-1)x+(root(6)(1+a)-1)=0` where `a gt -1`. Then, `underset(a rarr 0^(+))("lim") alpha(a) and underset(a rarr 0^(+))("lim") beta(a) are`

A

`- ( 5)/( 2)` and 1

B

`- ( 1)/( 2)` and -1

C

`- ( 7)/( 2)` and 2

D

`- ( 9)/( 2) ` and 3

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The correct Answer is:
B
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MOTION-LIMIT-EXERCISE-4
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  3. underset( x rarr 0 ) ( "lim")( (1- cos 2x) ( 3 + cos x ))/( x tan 4x) ...

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  7. For each t in R let [t] be the greatest integer less than or equal to ...

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  8. For x gt 0 , underset( x rarr 0) ( "Lim") [ ( sin x)^(1//x) + ((1)/( x...

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  9. Let L = lim(x rarr 0) ( a - sqrt( a^2 - x^2) - x^2/4)/x^4, a>0.If L is...

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  10. If underset( x to 0) lim [1+x log (1+b^(2))]^(1/x) = 2b sin^(2) the...

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  11. If underset( x rarr oo) ( "lim") (( x^(2) + x+ 1)/(x+1) -ax -b) = 4, t...

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  12. Let alpha(a) and beta(a) be the roots of the equation {(a+1)^(1//3)-1}...

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  13. The largest value of non-negative integer a for which underset( x rarr...

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  14. Let m and n be the two positive integers greater than 1 . If underset(...

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  15. Let alpha, beta in R such that lim(x ->0) (x^2sin(betax))/(alphax-sin...

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  16. Let f(x) = ((1 - x(1+ |1-x | )) /(|1-x|)) cos(1/(1-x)) for x!=1

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  17. Let f: R rarr R be a differentiable function with f(0)=0. If y=f(x) ...

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