Homework Statement
The function f(x)=5xarctan(3x) is represented as a power series. Find the first few coefficients in the power series.
Homework Equations
The power series is represented in the form sum(Cn*x^n)
The Attempt at a Solution
I've attempted to write the function as an...
Thank you! Everything works out perfectly after that.
So after integration by parts, I have:
I = f(x)*e^(-x/4) + (1/4)int f(x)*e^(-x/4)dx
Plug in the values and I have:
f(∞)e^(-∞/4) - 12e^(-1/2) + (1/4)(-8)
0 -12e^(-1/2) -2
Homework Statement
Let f(x) be a continuous function defined on the interval [2, ∞) such that
f(2) = 12
|f(x)| < x^8 + 8
and
⌠∞
f(x) * e^(−x/4) dx = −8
⌡2
Determine the value of
⌠∞
f′(x) * e^(−x/4) dx
⌡2 Homework Equations
The Attempt at a Solution
I started...