Recent content by Quireno

Will use the homework forum next time. Thank you, I can handle the problem from here.

Nevermind me, I'm just confused. Anyway, I have now the first part $$ \left|\left(1+\frac{\sin(u)}{2}\right)-\left(1+\frac{\sin(v)}{2}\right)\right|=\left|\frac{\sin(u)}{2}-\frac{\sin(v)}{2}\right|=\frac{|\sin(u)-\sin(v)|}{2}\leq \frac{1}{2}\left|u-v\right| $$ which can be proved by the mean...

Ok, I will try to do the exercise by treating the x as f(x). This could have been a misinterpretation of notation by myself. As for the expansion, I don't think it is neither necessary nor convenient.

Do you mean that the function does not matter? Maybe you are right, but can you explain further?

Thank you, but my problem persists: I am dealing with a general function here. Let's say ##u=x^{-1}## and ##v=y^{-1}##, now I have to prove that $$ \forall u,v \in\mathbb{R}\quad \left|f\left(1+\frac{\sin(u)}{2}\right)-f\left(1+\frac{\sin(v)}{2}\right)\right| \leq \frac{1}{2}\left|u-v\right| $$...

Hello everybody, I'm currently helping a friend on an assignment of his, but we are both stumbled on this exercise, I'm posting it here We define a function ##f## which goes from ##\mathbb{R}## to ##\mathbb{R}## such that its argument maps as $$ x \mapsto...

First: your normalization is correct. Second: My answer is not correct. The cosine function has to have negative values somewhere in its domain unless you have very specific conditions over ##T## and ##\dot{P}_0## -which were not given-. The negative values mean a negative population...

Hmm... let me check:P(t)=A\beta\cos\left(\frac{e^{-t/T}}{\dot{P_0}}\right)When the time is long enough (##t\rightarrow\infty##) my answer gives \lim_{t \to \infty}\frac{e^{-t/T}}{\dot{P_0}}=0\qquad\Rightarrow\qquad \lim_{t \to \infty}P(t)=A\beta\cos(0)=A\betawhich in essence is a constant. That...

This makes sense. That is exactly were I was confused at first! I opted to discard any dependence of ##\mu## with respect to age and instead make it a time-dependent mortality... the reason is that the main equation would depend on two variables and it seemed to over-complicate the problem. My...

Thanks to Ray and BvU for their replies. Although I couldn't manage to get clarifications from my teacher, and despite the fact the deadline was a week ago, I ought at least to answer you with the complete homework instructions (besides I'd like to know the answer ): 1. Homework Statement...

Homework Statement Let P(t) be a population at time t, b(t) is the birth rate at time t and d(t) is the death rate at time t. Define the relative mortality μ(t) as the probability to die at age t. How is it normalized? Set up an equation of the absolute number of deaths at time t as a...