Tagged Questions
4
votes
3answers
119 views
How $\frac{dx}{dy}=f(x)g(y) \Leftrightarrow \int \frac{dx}{f(x)} = \int g(y)dy$?
In my intro differential equations class we have often used the "equivalence" stated in title. It seems to me that somehow, the intermediate step $$ \frac{dx}{f(x)} = g(y)dy$$ is being used, in which ...
1
vote
0answers
104 views
Proving $f$ is constant.
Let $f$ and $g$ be continuous function where $f,g:[a,b] \rightarrow \Bbb R $
and $\int_a^b g(x)=0$ and $\int_a^b f(x)g(x)=0$ , show that $f$ is a constant function.
I tried a bunch of things ...
5
votes
1answer
52 views
Determining hyperreal class for $\frac{\epsilon + \delta}{\sqrt{\epsilon^2 + \delta^2}}$
I'm solidifying my calculus by going through Keisler's book that uses a hyperreal/infinitesimal approach. I'm stuck on this problem.
Given infinitesimals $\epsilon,\delta > 0$, deterimine whether ...
1
vote
1answer
136 views
little-o and its properties
I know that $f(x) = o(g(x))$ for $x \to \infty $ if (and only if) $\lim_{x \to \infty}\frac{f(x)}{g(x)}=0$ Which means than $f(x)$ has a order of growth less than that of $g(x)$.
1) I'm still ...
