InterviewSolution
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If|x|isso small thatx ^ 2andhigherpower ofx maybeneglectedthenan approximatevalue of((1 + (2 )/(3)x) ^(-3) (1 - 15 x ) ^(-1//5))/((2- 3x ) ^ 4)is |
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Answer» ` (1 )/(8) (1+ 7x ) ` `=(1 + (2 ) /(3) x ) ^(-3)( 1- 15x ) ^(-1/5) ( 2 - 3 x ) ^(-4 ) ` `= (1+(2)/(3) x ) ^(-3)( 1-15x ) ^( - 1/5 )2^(- 4 )( 1-(3x ) /(2) ) ^( - 4 ) ` NEGLECTING`x ^ 2`andhigherpowersof` .x.` `= (1)/(16)(1- 3((2)/(3)) x)(1- 15x(-1/5)) ( 1 +(3x ) /(2)(4)) ` `= (1 ) /(16)(1 - 2X ) (1 + 3x )( 1 +6x )` `= (1 ) /(16) (1 + x )(1 + 6x ) ` Neglecting`x ^ 2`andhigherpowersof `.x.` `=(1)/(16)( 1 +7x)` |
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