the series is (k!)^4/(4k)! i assumed we need to do the ratio test, but I don't know how to work with the factorials that result. I can't get most of them to cancel out. How do I tackle...
the series is (k!)^4/(4k)! i assumed we need to do the ratio test, but I don't know how to work with the factorials that result. I can't get most of them to cancel out. How do I tackle...
1+2r+r^2+2r^3+r^4+2r^5+r^6... We we only know how to work with basic geometric series at this point. We are told it converges for |r|<1 so I thought a/(1-r)...
x=2cos(t) y=1+2sin(t) 0<=t<=2pi To go halfway around counterclockwise starting at (0,3) you can change t: pi/2<=t<=3pi/2 I understand that, but it requires me...
integrate 1/(2-cos(x)) dx from 0-pi/2. Use the substitution t=tan(x/2)
Integrate (7+10cot(x))/(10-7cot(x)) from pi/4 to pi/2
When I substitute u=x^2-5x+25 I get du=2x-5 dx. That gets me close to x dx. I would normally just pull out 1/2, but I'm confused how to deal with the -5. it looks like I should get a ln...
A spherical tank is half full of oil that has a density of 900 kg/m^3. Find the work required to pump the oil out of the spout on top. Use 9.8 for g and 3.14 for pi. Round to 3 sig. figs. The...
Use cylindrical shells to compute the volume of a napkin ring of height 3h created by drilling a hole with radius r through the center of a sphere of radius R and express the answer in terms of h...
Sketch the region in the xy-plane defined by the inequalities x − 3y2 ≥ 0, 2 − x − 5|y| ≥ 0 and find its area. If I did it correctly, I have a region defined by x=3y^2, (x-2)/5, -(x-2)/5...
Y=8x^2 and x=8y^2 clearly (0,0) is one point of intersection. They should have another at I believe (1/8,1/8). How is that derived? TIA
Integral from 0-t of e^-x/(1+(e^-x)) dx I let u = e^-x and du=-e^-x dx. Then it is -1 times the integral of 1/ (1+u) du from 1 to e^-t which equals -(ln(1+u) from 1to e^-t which...
I need to integrate from 0-t. I am told to set u= Erf and u'= (2e^-x^2)/pi^1/2. v' is 1 and v=x. i am also told that the answer is t Erf(t)+ ((e^-t^2)-1)/pi^1/2 how many...
Calculate an expression for the int from 1 to e of (ln(x))^k dx in terms of the integral from 1 to e of (ln(x))^k-1 dx. essentially, I need to integrate by parts to get this equality: The...