Function of the Day: f(x)=e^x

tarnok

Diabloii.Net Member
Function of the Day: f(x)=e^x

This is something I plan to do with my students. Each day I'll post a _____ of the day on a small chalkboard to the side of the main one. Today it's a function. Tomorrow maybe a fruit. Whatever. It'll be something interesting and informative though, and sometimes just a little bit silly to keep them on their toes. I'd like to test them out here and see if people have anything to add or any suggestions for other _________s of the day.

If the mods think that one of these a day counts as spam just let me know and I'll discontinue post-haste.

So.

f(x)=e^x

This function, known as the exponential function, grows extremely rapidly. No, faster than that. To give you a rough idea of how fast it grows f(0)=1 while f(10) is over 22,000. Additionally e^x gets very small as x becomes more negative. It never actually reaches zero but it gets continually closer as x becomes more negative.
Points of interest:
f(-1)=1/e
f(0)=1
f(1)=e

bc10068

Diabloii.Net Member
geez.... i always wondered why there are so many smart people in DIABLO II -Otf forum...
Everyone is just so.... professional

masterazn

Banned
tarnok, what level math is this?

tarnok

Diabloii.Net Member
bc10068 said:
Everyone is just so.... professional
What posts have you been readin'?

Masterazn: It's honors algebra III. This isn't the kind of thing that will be on a test though anyway. Many of them said that they were in this class to prepare for higher math and this is partly a way to expose them to things that will be important for them in the future.

masterazn

Banned
I take Algebra II/Trig

I CAN DO THIS !!

Underseer

Diabloii.Net Member
More trivia:

d/dx (e^x) = e^x

Which in turn implies that the antiderivative is also e^x (+C of course). That makes this function mighty handy for simplifying things in higher math.

(Gripe: why can't we use named entities on this board? The above would've looked so much better if I could've used &part;

{KOW}Spazed

Banned
Well I have many odd facts just stored up for . . . I don't know why I just do!

The worlds largest flower is the Stink Corpse Lily and it is three feet wide has seven petals and its leaves are a quarter of an inch thick. The flower blooms every three years and smells like rotting meat to attract flies.

I have more things like that if you want. If you want more math related questions bust out the ninja-pirate questions. . . those where fun.

superman22

Diabloii.Net Member
here is some calculus posts!!!

the derivative of x^2 = 2x
the anti-derivative of x is x^2/2

then whats the derivative of lnx? 1/x of course!
wats the derivative of e^x ? e^x!
and the antiderivate of e^x? e^x silly!

if the derivative of sinx = cosx
then wats the derivative of cos x?

-sinx !!!!!!!

so heres a little quiz.... wats the derivative of x^3 + lnx -sinx ??

FoolioMcTavish

Diabloii.Net Member
I just learned all this in grade 12 calculus. This is easy.

Corneo

Diabloii.Net Member
tidbit:
e=1+1/1!+1/2!+1/3!+1/4!..+1/n! (n approaches inf.)
e= lim(n->inf) (1+1/n)^n
e=lim(n->0)(1+n)^(1/n)

Underseer

Diabloii.Net Member
This thread would be so much better if we could use HTML and named entities.

UBB is Satan's markup language! Down with UBB and this square bracket crap! *hoists protest sign*

Corneo

Diabloii.Net Member
I'm not sure if this site enables LaTeX or not, if it did I would be able to bust out with some hardcore looking functions.

Lone_C

Diabloii.Net Member
superman22 said:
here is some calculus posts!!!

the derivative of x^2 = 2x
the anti-derivative of x is x^2/2

then whats the derivative of lnx? 1/x of course!
wats the derivative of e^x ? e^x!
and the antiderivate of e^x? e^x silly!

if the derivative of sinx = cosx
then wats the derivative of cos x?

-sinx !!!!!!!

so heres a little quiz.... wats the derivative of x^3 + lnx -sinx ??
Bah, beginning Calc is easy.

3x^2 +1/x -cosx

asdf

Diabloii.Net Member
what's the integral of e^tan(x) ? i was never able to figure that one out... if there is an answer

mouschi

Diabloii.Net Member
I hate you all strictly because looking at those things makes my head explode. Good thing college algebra is all I need to get my degree, I hope.

Corneo

Diabloii.Net Member
Hey its got that Gabriel's horn aka Torricelli's trumpet on there!