Advertisements
Advertisements
Question
Find the coefficient of x4 in the expansion `(3 - 4x + x^2)/"e"^(2x)`
Advertisements
Solution
`(3 - 4x + x^2)/"e"^(2x) = (3 - 4x + x^2) "e"^(-2x)`
= `(3 -4x + x^2) [1 + (-2x)/(1!) + (-2x)^2/(∠2) + (-2x)^3/(∠3) ...]`
Coeffiient of x4: `3[(-2)^4/(4!)] - 4[(-2)^3/(3!)] + 1[(-2)^2/(2!)]`
= `3[16/24] + (- 4) ((- 8))/6 + 4/2`
= `48/24 + 32/6 + 2`
= `2 + 16/3 + 2`
= `(6 + 16 + 6)/3`
`28/3`
APPEARS IN
RELATED QUESTIONS
Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid
`1/(5 + x)`
Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid
`(5 + x^2)^(2/3)`
Write the first 6 terms of the exponential series
e5x
Write the first 6 terms of the exponential series
`"e"^(-2x)`
Write the first 4 terms of the logarithmic series
`log((1 - 2x)/(1 + 2x))` Find the intervals on which the expansions are valid.
If p − q is small compared to either p or q, then show `root("n")("p"/"q")` ∼ `(("n" + 1)"p" + ("n" - 1)"q")/(("n"- 1)"p" +("n" + 1)"q")`. Hence find `root(8)(15/16)`
Choose the correct alternative:
The coefficient of x6 in (2 + 2x)10 is
Choose the correct alternative:
The coefficient of x8y12 in the expansion of (2x + 3y)20 is
Choose the correct alternative:
If (1 + x2)2 (1 + x)n = a0 + a1x + a2x2 + …. + xn + 4 and if a0, a1, a2 are in AP, then n is
Choose the correct alternative:
If Sn denotes the sum of n terms of an AP whose common difference is d, the value of Sn − 2Sn−1 + Sn−2 is
Choose the correct alternative:
The sum up to n terms of the series `1/(sqrt(1) +sqrt(3)) + 1/(sqrt(3) + sqrt(5)) + 1/(sqrt(5) + sqrt(7)) + ...` is
Choose the correct alternative:
The coefficient of x5 in the series e-2x is
Choose the correct alternative:
The value of `1/(2!) + 1/(4!) + 1/(6!) + ...` is
Choose the correct alternative:
The value of `1 - 1/2(2/3) + 1/3(2/3)^2 1/4(2/3)^3 + ...` is
