Recent content by OrbsAndSuch

thank you for the help dx :!)

\frac{e^{x+1} - x - 2}{(x+1)^2} yes?

I would have to add the first two terms of the sum if the limits started at 0 which would be 1 + (x+1) 1 + (x+1) + \frac{e^{x+1}}{(x+1)^2} ?

I am having a similar problem myself in the above thread, but I do know that if you use the Ratio Test, and the outcome is less than one(i.e. zero) then the series converges, however this is NOT the sum. Past that i can't help. Sorry!

ok i factored and came up with: \frac{1}{(x+1)^2} \sum_2^\infty \frac{(x+1)^n}{n!} Do the indices matter? If not then it becomes \frac{e^{x+1}}{(x+1)^2}

yes, that's the expansion for ex. Its the (n+2)! in the original problem that's confusing me.

Hello, I need to find the sum(as a function of x) of the power series \Sigma^{\infty}_{n=0}\frac{(x+1)^n}{(n+2)!} The hint i was given was compare it to the Taylor series expansion of ex. Im not sure even how to start this problem and any help is much appreciated.

Hello, I am a freshman in college, and i have a while to pick my major, and eventually my career, but I figured I should start thinking now. Sorry if these questions seem completely random, but this how i think, and this series of questions has turned into a sort of half-rant, but any...

The formula for the area [ A = (1/2)*r2 ] effectively eliminates the square root, so i don't quite understand how its undefined from [pi/3, 2pi/3] because of the square root. However after proving to myself that r = 0 at 0 and pi/3, I have successfully found the area of one loop. Thanks...

Thank you Mark. Is finding the finding the area of the entire graph, then dividing that answer by the number of loops a viable method for this type of problem?

This is an extra credit problem for a take home test, so i will understand if no one feels comfortable helping me out, but any advice is greatly appreciated :biggrin: Homework Statement Compute the area enclosed by one loop of the graph given by r = sqrt(sin(3{theta})) Homework...