Recent content by RBG

OOOOOOHHHHH... duh. Nevermind. Right... Thanks! Just do the calculation of taking the derivative

I really don't understand what you mean by this. I should use the fact that I am minimizing ##|p-X(t)||## somehow to reduce the dot product?

You would take the derivative of ##||p-X(t)||## and minimize it. Then check which points are minimal, right?

We are assuming ##X(t)## is a regular parametrized curve and ##t_0## is not an endpoint of ##I##.

Dot product of the tangent vector, right? So above ##(p-X(t_0))## is the vector between point and curve and ##X'(t_0)## is the tangent vector. But I don't see why should ##p\dot X'(t_0)-X(t_0)X'(t_0)=0##

Isn't that the dot product is zero? That or that the slopes of the tangent lines are inverse reciprocals of one another. But I don't see how the latter definition can be applied...

Given a parametrized curve ##X(t):I\to\mathbb{R}^2## I am trying to show given a fixed point ##p##, and the closest point on ##X## to ##p##, ##X(t_0)##, the line between the point and the curve is perpendicular to the curve. My only idea so far is to show that...

Thank you!

Assume that ##\{f_n\}## is a sequence of monotonically increasing functions on ##\mathbb{R}## with ## 0\leq f_n(x) \leq 1 \forall x, n##. Show that there is a subsequence ##n_k## and a function ##f(x) = \underset{k\to\infty}{\lim}f_{n_k}(x)## for every ##x\in \mathbb{R}##. (1) Show that some...

I figured it out... how do I remove this question?

So if we're in the ##k=2## case and the only thing I know about ##f## is that it's continuous at ##0##, how would I show that ##f'(0)=M##?

Woops! Man, for a first post I am messing up a lot. I meant what my edits say, that is ##f(g(x))## not just ##g(x)## in the numerator!

Thank you! Also, I edited my question to what I meant. I am really more just interested in the ##g(x)=\frac{x}{k}## where ##k\in\mathbb{N}## case.

Homework Statement Warning: I realize the title is misleading... the function itself isn't what's constant. Mod note: Edited to fix the LaTeX If ##f## is a continuous at 0 such that ##\lim_{x \to 0}\frac{f(x)-f(g(x))}{g(x)}=M##, where ##g(x)\to 0## as ##x\to 0## does this generally mean that...