Hi. Any help with these would be much appreciated.
1. By considering the infinite series (SUMMATION SIGN with infinity on top and n=0 on bottom) of x^n for x< 1 show that:
(SUMMATION SIGN with infinity on top and n=0 on bottom) (n^2)(x^n) = x(1-x^2)/(1-x)^4.
I know this is to do with differentiating the previous derivative (x/(1-x)^2), but i got in a mess with it.
2.Find the indefinate integral of x^2*e^(x^3)
This is integration by parts but the x^3 is confusing me as i don't know how to deal with it. Basically my question is; how do you integrate e^(x^3)?
3. Use your calculator to find the value of the following expression when x=0.01 to 3dp:
y(x) = (e^(2x) - 2(1 +2x)^(1/2) +1) / (cos (x/2) -1)
The previous part of the question asked me to obtain Maclaurin series and re-write the above expression which i did. However when i substituted x=0.01 the 2 answers from the series and the exact did not match. I maybe approaching this question incorrectly. What is the meothod for this
Again any help would be much appreciated.
No need for integration by parts.
the substitution will solve it easily .
By the way, It is not easy to evaluate
since it has unelementary functions.
see this:
integrate e^(x^3) - Wolfram|Alpha