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Question

If x is small so that x2 and higher powers of x can be neglected then the approximate value for (12x)1(13x)2(14x)3

A
12x
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B
13x
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C
15x
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D
14x
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Solution

The correct option is D 14x
(12x)1(13x)2(14x)3

(12x)1(13x)2(14x)3
Since, x is very small, then (1+x)n=1+nx

(1+2x)(1+6x)(112x)
(1+6x+2x+12x2)(112x)
(1+8x+12x2)(112x)
1+8x+12x212x96x2144x3
14x84x2144x3
Since, we have to neglect higher power then, 84x2144x3=0
14x

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