Tagged Questions

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 ...
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 ...
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 ...
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 ...
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