Recent content by lxman

I have known for many years that the speed of sound (usually quoted ≈340 m/s) and the speed of light (usually quoted ≈3*10^8 m/s) are vastly different. Doing some reading, I would seem to conclude that part of the reason for this is the fact that sound is a mechanical wave, propagated through...

Alright then, let's see . . . eV is a unit of energy. Therefore would I be correct in concluding that the CO molecule has a quantity of energy closer to zero and therefore it would be more electrically stable?

Homework Statement As shown in class the electric potential energy of a water molecule is -5.33 eV. Which molecule is more electrically stable, H2O or CO? Why? Homework Equations EPE=Kc*q1*q2/r12 The Attempt at a Solution The water molecule's EPE is -5.33 eV. The carbon...

Okay, [0,14] did the trick. Thanks for hanging in there with me. I have a couple of questions still left. First off, the inclusion of zero in the set. The way that I am seeing it, the coefficients themselves make up a series which is alternating and decreasing (actually beginning with term...

Okay, I'm definitely not questioning you. Let me start from scratch with the problem definition directly from the homework and maybe I missed something or left something out. Represent the function f(x)=x^0.4 as a power series: \sum^{\infty}_{n=0}c_{n}(x-7)^{n} Find the following...

Hmm, thanks much for the help, but I tried giving that to my professor and he says "not correct." I thought it would be (6,8], but just in case I was wrong, I tried [6,8], [6,8) and (6,8). He's not agreeing with any of them. I thought I understood things all the way, but I'm confused again.

Nope, that should be: \left|\frac{1}{x-7}\right|<1 which tells me x>8 or x<6

Okay, so looking at what I have to work with, I can calculate that: \frac{a_{n+1}\ (x-7)^{.4-n-1}}{a_{n}\ 7^{.4-n}}=\frac{.4-n}{n+1}\ (x-7) Now, the ratio test is looking at \lim_{n\rightarrow\infty} which would be x-7. Therefore, I need \left|x-7\right|<1\Rightarrow 6<x<8, and I still...

Okay, that makes good sense. I have to define a center since depending on where I pick the center, the curve will be different and the interval of convergence will be different. So, my center is 7 in this case. What I understand from what you have written is that each successive numerator...

Homework Statement f(x)=x^{0.4} Construct a power series to represent the function and determine the first few coefficients. Then determine the interval of convergence. The Attempt at a Solution Determining the first few coefficients is simple enough. Take the first few...

Thank you all for your help.

Okay, yep, missed that one completely. Integrating gives me: \frac{7x^{3}}{3}-\frac{49x^{7}}{6} Now, plugging in 0.77, I get -0.245385 which is much closer. Again, I presume the error is from only using two terms.

SammyS, your idea sounds MUCH simpler, but you would have to explain the details of implementation to me. So, doing it the hard way - and yes, it gets a bit messy, so I won't post all the details. I end up with the first two non-zero terms being term 2, which evaluates to 14, and term 6, which...

The original problem statement says to use the first two terms of the Maclaurin series. So when I am constructing the series, I just basically throw away any terms with zero values, and the non-zero terms then become my series. Is this correct?

Homework Statement Assume that sin(x) equals its Maclaurin series for all x. Use the first two terms of the Maclaurin series for sin(7x^2) to approximate the integral: \int_{0}^{0.77}sin(7x^{2})\ dx The Attempt at a Solution If I understand correctly, a Maclaurin series is just a...