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comment Asymptote of solution of a differential equation without solving it
I don't really understand why it is sufficient to show that $u'(x) > 0$ for all $x$ and why this it the case. If $u'(x_0) = 0$ for some $x_0$, why is this automatically the case for all $x$?
Oct
18
revised Intiutive argument that $\exp' = \exp$
edited tags
Oct
15
revised Intiutive argument that $\exp' = \exp$
edited tags
Oct
15
comment Intiutive argument that $\exp' = \exp$
@mookid It's for a high school course. The real numbers are known only on a heuristic middle school level (via examples like $\sqrt{2}$ and $\pi$, nested intervals etc. Powers are introduced usually just for rational numbers and real powers via nested intervals (or sometimes just with reference to the calculater - which is really sad, but I don't have the time to rework those foundations, I just want to give a nice argument for the derivative of $\exp$ despite of the spongy foundations :-()
Oct
15
comment Intiutive argument that $\exp' = \exp$
But how to show that $\exp'(0) = 1$?
Oct
15
asked Intiutive argument that $\exp' = \exp$
Sep
23
revised Proof of continuity of Thomae Function at irrationals.
minor formatting improvement
Sep
23
suggested suggested edit on Proof of continuity of Thomae Function at irrationals.
Sep
23
awarded  Excavator
Sep
23
revised Proof of continuity of Thomae Function at irrationals.
improved formatting
Sep
23
suggested suggested edit on Proof of continuity of Thomae Function at irrationals.
Sep
13
awarded  Notable Question
Sep
10
asked Etymology of the word “function” in mathematics
Jul
24
revised Asymptote of solution of a differential equation without solving it
added 22 characters in body
Jul
24
comment Asymptote of solution of a differential equation without solving it
Would be nice if you could make it more rigerous
Jul
24
awarded  Yearling
Jul
24
asked Asymptote of solution of a differential equation without solving it
Jul
2
awarded  Curious
May
9
comment Proof: Force always perpendicular and motion in a plane implies that the trajectory is a circle
@DanielV No I mean that the force which corresponds to $x''$ and $x'$ which corresponds to the velocity are perpendicular.
May
9
revised Proof: Force always perpendicular and motion in a plane implies that the trajectory is a circle
added 144 characters in body