1.

If(x - 4 )/( x^ 2 - 5x+6)canbeexpandedintheascendingpowersofx,thenthe coefficientofx ^ 3is

Answer»

` ( - 73 )/(648) `
`(73)/(648) `
`(71)/(648) `
` ( - 71)/(648)`

Solution : `(x -4) / ( x ^ 2- 5x+ 6 ) `
`=(2 ) /((x - 2 )) - (1)/((x - 3 )) `
`therefore(2) /((x - 2 )) - (1)/((x-3))= (2)/((-2) (1 - (x ) /(2)) )+(1)/(3(1 -(x)/(3)) `
=` (1 ) /(3) (1 -(x )/(3)) ^( -1)- (1 -(x)/(2)) ^(-1) `
`=(1)/(3) [ 1+(x)/(3)+((x)/(3)) ^ 2+ (x/3)^ 3 +... ] `
` - [ 1+(x )/(2)+ (x/2) ^2+(x/2 ) ^ 3+... ] `
`therefore`CO - efficientof`x ^ 3` inaboveexpansion is
` (1)/(3)(1/3) ^3- (1/2) ^3 = (1)/(81)- (1)/(8)= ( -73)/(648) `


Discussion

No Comment Found

Related InterviewSolutions