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If ((1-3x)^(1//2)+(1-x)^(5//3))/(sqrt(4-...

If `((1-3x)^(1//2)+(1-x)^(5//3))/(sqrt(4-x))` is approximately equal to `a+bx` for small values of `x`, then `(a,b)=`

A

`(1,(35)/(24))`

B

`(1,-(35)/(24))`

C

`(2,(35)/(12))`

D

`(2,-(35)/(12))`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `((1-3x)^(1//2)+(1-x)^(5//3))/(2[1-(x)/(4)]^(1//2))`
`=([1+(1)/(2)(-3x)]+[1+(5)/(3)(-x)])/(2[1+(1)/(2)(-(x)/(4))])`
(Neglecting higher powers of `x`)
`=([1-(19)/(12)x])/([1-(x)/(8)])`
`=[1-(19)/(12)x][1-(x)/(8)]^(-1)`
`=[1-(19)/(12)x][1+(x)/(8)]=1-(35)/(24)x`
then `a+bx=1-(35)/(24)ximpliesa=1`, `b=-(35)/(24)`
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