anonymous
  • anonymous
is e (mathematical constant) called as exponential?
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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experimentX
  • experimentX
called euler's constant
TuringTest
  • TuringTest
To say the phrase "e is exponential" makes no sense. E is "Euler's constant, which is transcendental, similar to \(\pi\))
experimentX
  • experimentX
truely TRANSCENDENTAL indeed

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anonymous
  • anonymous
then what is exponential growth, doesn't it involve e?
TuringTest
  • TuringTest
it has the special property that as an exponential base, we have that\[\int e^xdx=\frac d{dx}e^xdx=e^x(+C)\]and has all kinds of crazy things associated with it that you will learn by just encountering it again and again
TuringTest
  • TuringTest
typo-ed that up pretty bad...
TuringTest
  • TuringTest
\[\int e^xdx=\frac d{dx}e^x=e^x\](ignoring the plus C thing...)
TuringTest
  • TuringTest
...the point is that it just comes up in nature and math friggin' \(everywhere\), which is what I think @experimentX was referring too by how it is truly "transcendental".
experimentX
  • experimentX
@TuringTest does lim n->inf (1+r/(n*100))^n = e
experimentX
  • experimentX
oops that was a question
TuringTest
  • TuringTest
let's try it shall we?
experimentX
  • experimentX
sure ... and do you know where it comes from??
TuringTest
  • TuringTest
hey did you mean n when you said r experiment?
TuringTest
  • TuringTest
or 1 maybe?
anonymous
  • anonymous
@TuringTest instead of posting another question can you please help me with another question i.e. at http://tutorial.math.lamar.edu/Classes/DE/Linear.aspx in example number 6, after doing the integration part on int 2e^-t/2 sin(3t) dt , where did this -24/37 has come from. thanks in advance
experimentX
  • experimentX
no ... it's the (maximum) compound amount ... that can be collected for given interest rate
TuringTest
  • TuringTest
so we treat it as a constant?
TuringTest
  • TuringTest
\[\lim_{n\to\infty}(1+\frac r{100n})^n\]\[=\large e^{\lim_{n\to\infty}\ln(1+\frac r{100n})^n}\]just looking at the exponent\[\lim_{n\to\infty}n\ln(1+\frac r{100n})=\lim_{t\to0}{{\ln(1+\frac {rt}{100}})\over t}\]looks like we need l'Hospital...
anonymous
  • anonymous
:|
TuringTest
  • TuringTest
ok I will stop and answer wounded's question :P
experimentX
  • experimentX
okay, i will post it as question
experimentX
  • experimentX
but first ... let's do wonded's question
anonymous
  • anonymous
are we suppose to take u=sin(3t) and dv=2e^-t/2 ?
TuringTest
  • TuringTest
I think it can be done either way
anonymous
  • anonymous
please, can you please show me the steps?
TuringTest
  • TuringTest
that's what I'm typing :)
experimentX
  • experimentX
wolfram has the same answer .. i hate to do this especially i'm so worst at latex, and you have to integrate by parts twice
TuringTest
  • TuringTest
yeah I'm just doing it with latex for kicks. I guess I'm bored, lol
anonymous
  • anonymous
i just got stuck in a circle :(
TuringTest
  • TuringTest
that is what is supposed to happen
experimentX
  • experimentX
can anyone find formula for integration of e^ax sin bx
experimentX
  • experimentX
= e^ax(asin(bx) - b cos(ax))/(a^2+b^2)
experimentX
  • experimentX
just use that values a=(-1/2) and b=3, you will get the answer
TuringTest
  • TuringTest
I keep getting booted :( m almost done trying to answer wounded first
experimentX
  • experimentX
are you trying to derive formula? I am about to post question
experimentX
  • experimentX
@TuringTest my question is somewhat like this Compound amount problem: Let for amount A, and r per year, what is the maximum compound amount that can be generated if it is allowed to be compounded in any interval of time as it wished. anywhere to improve??
TuringTest
  • TuringTest
oh man, sorry but those interest problems always give me headaches @Zarkon may be interested in helping

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