Recent content by Rudeboy37

Btw, you originally mentioned the derivative of (sinx)/x at x=0. However, does it even make sense to talk about the derivative at x=0? What must be true for the derivative to even exist at a certain x-value?

Mainly people "like L'Hopital's so much" because many people learn L'Hopital's in Calculus I where as Taylor Series is usually saved for a Calculus II class. Also, many books (like Stewart and Rogawski) cover L'Hopital's at least a couple chapters before Taylor Series are even mentioned. Most...

Be careful about this type of logic. 0/0 (one thing divided by the same one thing) doesn't always equal one. Hence the reason why we have L'Hopital's rule. Different examples of "0/0" not equaling 1: lim x->0 (sinx)/(x^3)=infinity lim x->0 (sinx)/(x^2)=DNE lim x->0 (x^2)/(sinx)=0

This is correct, but 0 nor 0,0 are positive integers. Remember that n*1 means 1+1+...+1 n-times. Basically, you can think of n*1 as 1^n in the underlying additive group. The characteristic of a ring can also be thought of as the order of 1 (the multiplicative identity element) in the...

Yes, so what are the characteristics of your two rings? Are they the same?

Homework Statement Does the integral from 1 to infinity of ([(Cos[Pi x])^(2x)]/x)dx converge? Homework Equations N/A The Attempt at a Solution I claim it converges (based on how small the values of the function get when x is not an integer), but I'm not really sure how to...

And come to think of it, my integral test doesn't work since this is not decreasing. Losiu99, where does the sqrt3 come from?

I don't think such function exists. Proof: Assume such function f(n) exists. Since integral from 1 to infinity converges, the integral test tells us that the sum from 1 to infinity also converges. This contradicts the fact we want the sum to diverge. Therefore no such function exists.

The axis you are rotating around DOES matter! When you rotate around an axis that's far away from your region, the shape and volume of the object is changing compared to an axis that's flush with your region. The basic formula for shells is integral of 2pi*radius*height. When your axis is...

Homework Statement Sum from 1 to infinity of [(sin n)^2]/n^(1/2) Homework Equations The Attempt at a Solution I've tried every basic series test: Test for Divergence: the limit approaches 0 so that doesn't tell us anything Direct Comparison test: its smaller than...

I would suggest looking at the characteristic of each ring (i.e., the order of 1 in the underlying additive group) If rings (or groups) are isomorphic, what must be true about their characteristics (or orders of elements)?