Recent content by aid

What method is possible to apply in this case, then? Is it really so that the Thevenin equivalent voltage of the marked part is equal to: V_{oc} = 12 \angle0 V?

Homework Statement I am attempting to solve problem number 4 from the following picture: http://img641.imageshack.us/img641/7950/imageisx.jpg In the picture you can see the suggested line of "cut" for the first application of Thevenin's theorem. The Attempt at a Solution I...

Hi there, I've been wondering for some time what the nuclear engineer job exactly looks like. I am particulary interested in one question: is there a place in the field of nuclear engineering for guys who would rather do the math and equations than build anything? Are there jobs for power...

Hi there, I've been wondering for some time what the power engineer job exactly looks like. I am particulary interested in one question: is there a place in the field of power engineering for guys who would rather do the math and equations than build anything? Are there jobs for power...

So, I was wondering what is the best possible way to become a climatologist. Having to deal with all that data concerning climate seems like a fun idea to me. Is becoming a specialist in climate science an option after getting bachelor's degree in mathematics? If yes, what should one be...

Homework Statement Compute the limits: a) \lim_{n \rightarrow \infty} n(2\sqrt{n^2 - n + 2} - 3\sqrt{n^2 + 1} + \sqrt{n^2 + 2n}), b) \lim_{n \rightarrow \infty} n(n + 4\sqrt{n^2 + n} - 2\sqrt{n^2 - n} - 3\sqrt{n^2 + 2n}). The Attempt at a Solution Well, dividing by n^2 leads...

I'm confused: this article - http://kbeanland.files.wordpress.com/2010/01/beanlandrobstevensonmonthly.pdf (proposition 3.1 to be exact) - clearly implies that there are some x \notin \mathbb{Q} such that f'(x) doesn't exist. :/

For a given f and a number a the derivative is the limit: \lim_{h \rightarrow 0} \frac{f(a + h) - f(a)}{h} So, in this case the derivative at a given irrational a would be: f'(a) = \lim_{x \rightarrow a} \frac{f(x)}{x - a}, x \in \mathbb{Q} But (from Heine's definition of a limit)...

Well, given q \in \mathbb{N}, the statement of yours is equivalent to the existence of p \in \mathbb{Z} such that: aq - \frac{1}{2} < p < aq + \frac{1}{2} The latter is quite obvious since a \notin \mathbb{Q}. The rest of your message, however, remains unclear to me. I understand that a...

I'm not asking for it either. Should the validity of the statement be seen out of the definition, i.e. \lim_{x\rightarrow a}{\frac{f(x)-f(a)}{x-a}}= \lim_{\frac{p}{q} \rightarrow a} \frac{1}{q} \cdot \frac{\frac{1}{q}}{\frac{p}{q} - a} ? As you've pointed, \frac{1}{q} \rightarrow 0, but...

Well, if \delta \rightarrow 0, then the denominators \rightarrow \infty, is that right? Still don't see how this is going to suffice for the proof. :/

I've tried to prove it straight from the definition of a derivative but it turns out not to be so easy. Any hints on how exactly should I do that?

Homework Statement Let's take function given by a condition: f(x) = \begin{cases} \frac{1}{q^2} \ iff \ x = \frac{p}{q} \ $nieskracalny$,\\ 0 \ iff \ x \notin \mathbb{Q} \end{cases} Prove the existence of the derivative of f in all points x \notin \mathbb{Q}. The Attempt at a...

Homework Statement So, I am to calculate limit of a sequence given by a formula: \sum^{n}_{i = 1} \sum^{i}_{j = 1} \frac{j}{n^3} The Attempt at a Solution I've tried to write down the sequence explicite and this is what I get: \frac{1}{n^3} + (\frac{1}{n^3} + \frac{2}{n^3}) + ... +...

Homework Statement Calculate the limit of a given sequence for n \rightarrow \infty: \frac{1 - 2 + 3 - ... + (2n - 1) - 2n}{\sqrt{n^2 + 1}}The Attempt at a Solution The correct answer seems to be -1. I've tried to apply the Stolz theorem but failed to compute \sqrt{(n + 1)^2 + 1} - \sqrt{n^2...