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Ifxisnumericallysosmall sothatx ^ 2andhigherpowersofxcanbeneglected,then(1 +(2x )/(3)) ^(3//2). (32 +5x) ^(-1//5)isapproximatelyequalto |
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Answer» ` (32 +31 x)/(64)` `=(1 + (2x ) /(3)) ^(3/2)(32 ) ^(-1/5) [ 1+(5x ) /( 32 ) ]^( -1//5 ) ` `=[ 1+(3 ) /(2)((2x ) /(3)) + …. ] ((1 )/(2)) [1- (5x ) /(32) ((1)/(5))+… ]` byneglecting `x^ 2`TERMS `= [1 + x ][ (1)/(2) ][ 1- (x )/(32)] ` `= (1)/(2)[ 1 -(x)/(32)+ x - (x ^ 2 )/(32) ] ` Byneglecting `x ^ 2`terms, we get, ` = (1)/(2) [ 1 +(31x)/(32)] ` `= (32 + 31 x ) /(64) ` |
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