Question

The constant term in the expansion of `(3^(x)-2^(x))/(x^(2))` is
A. `log_(e)3`
B. `(log_(e)6)xx{(log_(e))(3/2)}`
C. `1/2(log_(e)6)xx{(log_(e))(3/2)}`
D. none of these

Answer 1

Answer:
We have
`(3^(X)-2^(y))/(x^(2))=(1)/(x^(2))[{1+x(log_(e)3)+(xlog_(e)3)^(2)/(2!)+….}`
`-{1+x(log_(e)2)+(xlog_(e)2)^(2)/(2!)+…}]`
`therefore "constant term" =(log_(e)3)^(2)/(2!)-(log_(e)2)6(2)/(2!)`
`=1/2(log_(e)3+log_(e)2)(log_(e)3-log_(e)2)=1/2(log_(e)6)log_(e)(3/2)`

Answer 2

Correct option is (C)

Hence the term with x² in 3^x - 2^x will be

Dividing by x², we get

\(In(6)In(\frac{3}{2})\frac{1}{2}\)