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Question

If x is so small that x3 and higher powers of x may be neglected, then (1+x)3/2(1+12x)3(1x)1/2 may be approximated as ___________________.

A
x238x2
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B
38x2
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C
3x+38x2
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D
138x2
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Solution

The correct option is B 38x2
(1+x)3/2(1+12x)3(1x)1/2

(1+x)32(1+x2)3(1x)12


(1x)12⎢ ⎢ ⎢⎜ ⎜ ⎜1+32x+32.122!x2⎟ ⎟ ⎟(1+3x2+3.22!x24)⎥ ⎥ ⎥

⎢ ⎢ ⎢1+x2+12.322!x2⎥ ⎥ ⎥[38x2]
It is given that x is small so x3 and higher power can be neglected.

38x2

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