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If lim(xrarr0)(x^3)/(sqrt(a+x)(bx-sinx))...

If `lim_(xrarr0)(x^3)/(sqrt(a+x)(bx-sinx))=1,agt0`, then `a+b` is equal to

A

36

B

37

C

38

D

40

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(xrarr0)(lim)(x^(3))/(sqrt(a+x)(bx-sinx))=1`
`rArr" "underset(xrarr0)(lim)(x^(3))/(sqrta(bx-sinx))=1`
`rArr" "underset(hrarr0)(lim)(3x^(2))/(sqrta(b-cos x))=1`
`therefore" "b=1`
`therefore" "l=underset(xrarr0)(lim)(3x^(2))/(sqrta(1-cosx))`
`" "=underset(xrarr0)(lim)(3x^(2))/(sqrta 2sin^(2).(x)/(2))=(6)/(sqrta)`
`therefore" "a=26`
Thus `a+b=37`
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