1.

Ifxisnumericallysosmall sothatx ^ 2andhigherpowersofxcanbeneglected,then(1 +(2x )/(3)) ^(3//2). (32 +5x) ^(-1//5)isapproximatelyequalto

Answer»

` (32 +31 x)/(64)`
`(31 +32 x ) /(64) `
` (31 - 32 x ) /(64) `
` (1 - 2x )/(64) `

Solution : `(1+(2x ) /(3) ) ^( 3/2)(32 +5X ) ^( -1/5 ) `
`=(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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