- #1
Meaghan26
- 2
- 0
Hi everyone! I'm new here but I really hope you guys can be of some more help then my professor. We have our final exam next week (class ended today!) and the following 2 questions are on our review sheet. However, we NEVER covered this material. I'm terrible at "self taught" math so I'm having trouble here. My professor has office hours next week that I plan on attending but she did say specifically that we need to know everything on here. Okay so here they are:
1.Find the interval of convergence for the series:
Summation(1 to infinity) of
(2^(k)) / ((2k)!) * x^(k)
2.Write the first five nonzero terms in a power series for
x / (2+3x^(3))
Find the interval of convergence. Use these five terms to estimate:
Integral from 0 to 0.1 (xdx) / (2+3x^(3))
Okay so I'm figuring for the first one, you do the ratio test on the k terms so you end up with just x's but I'm not sure how you exactly calculate the interval. I see in my book something about setting up an inequality with x less than 1 and greater than -1 but is this standard?
And with the second one, we've never done anything with power series so I'm completely at a loss. I see in my book again that you take the derivatives of f(x) to calculate the c's plugging in 0 for x but really again, I don't know if that's standard or just for the examples I've seen.
So I'm pretty much at a huge loss - help!
Thank you
1.Find the interval of convergence for the series:
Summation(1 to infinity) of
(2^(k)) / ((2k)!) * x^(k)
2.Write the first five nonzero terms in a power series for
x / (2+3x^(3))
Find the interval of convergence. Use these five terms to estimate:
Integral from 0 to 0.1 (xdx) / (2+3x^(3))
Okay so I'm figuring for the first one, you do the ratio test on the k terms so you end up with just x's but I'm not sure how you exactly calculate the interval. I see in my book something about setting up an inequality with x less than 1 and greater than -1 but is this standard?
And with the second one, we've never done anything with power series so I'm completely at a loss. I see in my book again that you take the derivatives of f(x) to calculate the c's plugging in 0 for x but really again, I don't know if that's standard or just for the examples I've seen.
So I'm pretty much at a huge loss - help!
Thank you