Recent content by Hummingbird25

I have question. If we take an ordernary nuclear bomb and inject anti-matter into the core, and find a way to isolate the matter/antimatter reaction from the rest of detonation. Would it be possible to use force of the nuclear bomb to generate a black hole and thereby vaporize an entire...

thanks maybe you would look at https://www.physicsforums.com/showthread.php?t=218339 And maybe comment on my three proofs here ? Thanks in advance. Best Regards Maria.

Okay and thank your for your answer, Here we go again: proof: By applying the limit sin(t)/(t+n*pi)>sin(t)/(t+(n+1)*pi) the integrand becomes positive for all n. The integral is positive and inequality is thusly true. How about now? Best Regards. Maria.

Here is my original proof: Looking at the Integral a_n = \int_{0}^{\pi} \frac{sin(x)}{x+n\pi} prove that a_n \geq a_{n+1} Homework Equations The Attempt at a Solution Here is my now proof: the difference between the two integrals, we seek to show: $\forall...

And thusly it converges? Sincerely Maria.

Hi Dick, So I change my conclusion. Since sin(t) is positive on the interval [0,pi] then the who integral most be positive and thusly convergent. Does this sound better? Sincerely Maria

This is a repost, the reason I feared that people who miss the the original. Homework Statement Looking at the Integral a_n = \int_{0}^{\pi} \frac{sin(x)}{x+n\pi} prove that a_n \geq a_{n+1} Homework Equations The Attempt at a Solution Here is my now proof: the...

Hi Regarding Proof(1) \mathop{\lim} \limit_{n \to 0} \frac{sin(x)}{x} = 0 therefore the integral \int_{0}^{1} \frac{sin(x)}{x} converges. Regarding Proof(2) How would you recommend aproaching it? If not by the comparison test? Regarding Proof(3) Oh :-( I really thought I had it. How...

How would you recommend that I change then to make it more understandable? "No it isn't. It's just that you wrote |sin x| / x > 1/x when it should be |sin x| / x < 1/x. See comment above." Proof(2): So basic I say. By the result in (1), then the integral diverges by the comparison test |sin x|...

I treat the first integral as a p-series where p = 1 and from this conclude that that integral is convergent. I will change that Would say its wrong to use the comparison test here? You mean I shold say that RHS integral is divergent by the comparison test? Sincerely Maria

Homework Statement Case (1) Given the Dirichlet Integral I = \int_ {0}^{\infty }\frac{sin(x)}{x} dx Prove that this is convergent. Case(2) Given the Dirichlet Integral I = \int_ {0}^{\infty }\frac{|sin(x)|}{x} dx prove that it is divergent. case(3) Given the series I = \int_ {0}^{n...

Here is my now proof: the difference between the two integrals, we seek to show: $\forall n\in\mathbb{N}:\int_0^\pi\left({\sin t\over t+n\pi}-{\sin t\over t+(n+1)\pi}\right)\,dt\ge 0 Common denominator: $=\int_0^\pi\left({\sin t((t+(n+1)\pi)-(t+n\pi))\over (t+n\pi)(t+(n+1)\pi)}\right)\,dt...

Integral test by comparison(Please look at my work) Homework Statement Looking at the Integral a_n = \int_{0}^{\pi} \frac{sin(x)}{x+n\pi} prove that a_n \geq a_{n+1} Homework Equations The Attempt at a Solution Proof given the integral test of comparison and since...

I get it now. I will present something that I have been working later I hope you will review.

Integral inequality and comparison Homework Statement Prove the inequality \frac{2}{(n+1) \cdot \pi} \leq a_n \leq \frac{2}{n \pi}} where a_n = \int_{0}^{\pi} \frac{sin(x)}{n \cdot \pi +x} dx and n \geq 1 The Attempt at a Solution Proof: If n increased the left side of...