Question

is e (mathematical constant) called as exponential?

Answer 1

called euler's constant

Answer 2

To say the phrase "e is exponential" makes no sense.
E is "Euler's constant, which is transcendental, similar to \(\pi\))

Answer 3

truely TRANSCENDENTAL indeed

Answer 4

then what is exponential growth, doesn't it involve e?

Answer 5

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

Answer 6

typo-ed that up pretty bad...

Answer 7

\[\int e^xdx=\frac d{dx}e^x=e^x\](ignoring the plus C thing...)

Answer 8

...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".

Answer 9

@TuringTest does lim n->inf (1+r/(n*100))^n = e

Answer 10

oops that was a question

Answer 11

let's try it shall we?

Answer 12

sure ... and do you know where it comes from??

Answer 13

hey did you mean n when you said r experiment?

Answer 14

or 1 maybe?

Answer 15

@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

Answer 16

no ... it's the (maximum) compound amount ... that can be collected for given interest rate

Answer 17

so we treat it as a constant?

Answer 18

\[\lim_{n\to\infty}(1+\frac r{100n})^n\]\[=\large e^{\lim_{n\to\infty}\ln(1+\frac r{100n})^n}\]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...

Answer 19

:|

Answer 20

ok I will stop and answer wounded's question :P

Answer 21

okay, i will post it as question

Answer 22

but first ... let's do wonded's question

Answer 23

are we suppose to take u=sin(3t) and dv=2e^-t/2 ?

Answer 24

I think it can be done either way

Answer 25

please, can you please show me the steps?

Answer 26

that's what I'm typing :)

Answer 27

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

Answer 28

yeah I'm just doing it with latex for kicks.
I guess I'm bored, lol

Answer 29

i just got stuck in a circle :(

Answer 30

that is what is supposed to happen

Answer 31

can anyone find formula for integration of e^ax sin bx

Answer 32

= e^ax(asin(bx) - b cos(ax))/(a^2+b^2)

Answer 33

just use that values a=(-1/2) and b=3, you will get the answer

Answer 34

I keep getting booted :(
m almost done trying to answer wounded first

Answer 35

are you trying to derive formula? I am about to post question

Answer 36

@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??

Answer 37

oh man, sorry but those interest problems always give me headaches
@Zarkon may be interested in helping