1.

If|x|isso small thatx ^ 2andhigherpower ofx maybeneglectedthenan approximatevalue of((1 + (2 )/(3)x) ^(-3) (1 - 15 x ) ^(-1//5))/((2- 3x ) ^ 4)is

Answer»

` (1 )/(8) (1+ 7x ) `
` (1 )/(16) (1 - 7x ) `
`1-7x `
`( 1 )/(16) (1 + 7x ) `

Solution : ` (( 1 +(2 ) /(3)x )^( -3) (1 -15 x ) ^(-1/5))/((2 - 3X ) ^(4 ))`
`=(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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