How do you derive a power series for:
a.) xsinhx
b.) ∫ln(3t)dt from (1/3) to x
c.) ∫(9)/(t^(2)+3)dt from 0 to x
d.) (d/dx)(cosx^(0.5))
e.) e^(2x) in 2 ways
f.) f(x)=e^(x^2) and fin f^(12)(0)
g.) xe^(x) centered at 0 and use this representation to find the sum of the infinite series ∑ (1)/(n!(n+2)) from n=1 to ∞
h.) the dericative of the power series in g and use the result to find the sum of the infinite series ∑ (n+1)/(n!) from n=0 to ∞

Question

How do you derive a power series for:
a.) xsinhx
b.) ∫ln(3t)dt from (1/3) to x
c.) ∫(9)/(t^(2)+3)dt from 0 to x
d.) (d/dx)(cosx^(0.5))
e.) e^(2x) in 2 ways
f.) f(x)=e^(x^2) and fin f^(12)(0)
g.) xe^(x) centered at 0 and use this representation to find the sum of the infinite series ∑ (1)/(n!(n+2)) from n=1 to ∞
h.) the dericative of the power series in g and use the result to find the sum of the infinite series ∑ (n+1)/(n!) from n=0 to ∞

anonymous · Answer

is this your homework?

anonymous · Answer

Yeah, but I don't know how to do any of it so some tips or advice would be nice.

experimentx · Answer

one at a time!!!

anonymous · Answer

http://en.wikipedia.org/wiki/Taylor_series#Definition

experimentx · Answer

sinhx = (e^x - e^-x)/2
if you know the expansion of e^x and e^-x, then you can do 1)

anonymous · Answer

Some helpful advice, but the problem is I don't understand what the question is asking so I don't know how to start.

experimentx · Answer

for first, expand e's

anonymous · Answer

What do you mean by expand?

experimentx · Answer

http://www.math.com/tables/expansion/exp.htm

anonymous · Answer

So you basically memorize the expansion form of e in order to do that problem?

experimentx · Answer

yeah ... better if you learn taylor's or maclaurin expansion of function.

anonymous · Answer

What are those?