Take the 2-minute tour ×  I want to show that for $\gamma: [a,b]
\subseteq \mathbb{R} \rightarrow V$ continously differentiable
where V is a bounded subset of $\mathbb{R}^2$. There is always a
sequence of functions $f_n:\mathbb{R} \rightarrow \mathbb{R}$
that approximates this curve if we assume that for
$\gamma(t)=(x_1(t),x_2(t))$ we have $\dot{x}(t)\ge0$. Is there a
theorem that could help me with this?  share|improve this
question Depends on what you mean by approximating? I could use
$\gamma$ to approximate $\gamma$, but that's quite lame. What
properties do you want your approximation to satisfy? Also, it
doesn't make sense to ask that the derivative is positive
considering it has to be a vector. –  Patrick Da Silva Mar 15
'13 at 19:04 I can approximate any continuous function by an
infinity differentiable one (in the sup-norm). –  Baby Dragon
Mar 15 '13 at 19:10 what is the name of your theorem? did you
keep in mind that i have a curve in two dimensional space, but
want to approximate it by an actual fu