# calculus ii

1. ### Limits of sequences involving factorial statements!

Homework Statement I have to determine whether or not the following sequence is convergent, and if it is convergent, I have to find the limit. an = (-2)n / (n!) In solving this problem, I am not allowed to use any form or variation of the Ratio Test. 2. The attempt at a solution I was...
2. ### Integrating Using a Substituation

Homework Statement Use the substitution $u=\frac{\pi} {2}-x$ evaluate the integral $\int_0^\frac {\pi}{2} \frac {\sin x}{\cos x + \sin x}dx$. Homework Equations [/B] $\cos (\frac {\pi}{2}-x)=\sin x$ The Attempt at a Solution [/B]I start by plugging "u" into the equation making the...
3. ### Calculus 2 integrals

Homework Statement Here are the problems http://imgur.com/a/kbtPS The problems I need help with are 1 and 4(a) Homework Equations The second fundamental theorem of calculus The Attempt at a Solution For problem 1, I calculated the areas under the curve (using remmien summs) and tried to find...
4. ### Volume of a Solid Revolved About X-Axis

I'm trying to practice for my final. The sample problem is: "Find the volume of the solid generated when the region bounded by y = x4and y = x1/3, 0<=x<=1, is revolved about the x-axis." To start, I set the two y equations equal to each to find the points of intersection. x4 = x1/3, : raise...
5. ### Representing functions as power series

Homework Statement I have this function f(x) = \frac{6}{1+49x^2}, and i suppose to represent this function as a power series \displaystyle f(x) = \sum_{n=0}^\infty c_n x^n. Then i need to find the first few coefficients in the power series. Homework Equations The Attempt at a Solution...
6. ### Arc length problem calc II

Homework Statement Find the exact length of the curve: y= 1/4 x2-1/2 ln(x) where 1<=x<=2 Homework Equations Using the Length formula (Leibniz) given in my book, L=Int[a,b] sqrt(1+(dy/dx)2) I found derivative of f to be (x2-1)/2x does that look correct? The Attempt at a Solution I found f'...