Recent content by calcboi

So do I use 3 different curves then since you gave me a piecewise function? Like for one I use 6cos(theta) and so on.

Length of a Polar Curve L = integral from a to b of square rt(r^2 + (dr/dtheta)^2) dtheta

I can't find T unless I have an angle for theta, and I don't know what to put for the angle. I am guessing I should use 15 degrees from the earlier portion but I'm not sure.

Yes, I have the formulas and I got the area already. I have the polar arc length formula but it only works when there is one curve, just one r. I have r1 and r2, two different curves, and I am unsure how to calculate the arc length with two polar curves.

Thanks, but I am unsure what to use for the limits of integration.

I found the intersection points to be 2pi/3 to 4pi/3. If I divided the length around the intersection into 3 curves, I could find the area from the curve to the origin if I knew the equation of each one. I don't understand how to come up with one polar equation to solve for the intersection or...

The centerfield fence at a ballpark is 10 ft high and 400 ft from home plate. The ball is 3 ft above the ground when hit, and leaves with an angle theta degrees with the horizontal. The bat speed is 100 mph. Use the parametric equations x = (v0cos(theta))t y = h + (v0sin(theta))t - 16t^2 a...

Sketch the 2 polar curves r = -6cos(theta), r = 2 - 2cos(theta). a. Find the area of the bounded region that is common to both curves. b. Find the length around the intersection of both curves. I got a, but I don't know what to do for b because in my calculus book it only shows how to find the...

I am trying to determine convergence for the series n=1 to infinity for cos(n)*pi / (n^2/3) and I am doing the Ratio Test. I found the limit approaches 1 but is less than 1. Does this mean that the limit = 1 or is < 1? I am somewhat confused since this changes it from inconclusive to convergent.

When I tried the Limit Comparison Test, I got infinity as n approaches infinity. How did you get 1?

What test did you use to determine absolute convergence? Or was that just analyzing end behavior?

BTW, I used the comparison c(x) = 1/n^3 for DCT and LCT since we know 1/n^3 converges by p-series.

I have a question on which test to use for series n=1 to infinity for (-1)^n / (n^3)-ln(n) in order to determine convergence/divergence. I am pretty sure I determined it converges through the Alternating Series Test(correct me if I'm wrong) but I am not sure whether it is conditional or...

Oops, sorry. I will ask the question in the Calc thread.

Thanks, I see how that works if its a constant. Anyways, I have a question on which test to use for series n=1 to infinity for (-1)^n / (n^3)-ln(n) in order to determine convergence/divergence. I am pretty sure I determined it converges through the Alternating Series Test but I am not sure...