Question

Taylor series for sinx centered at (pi)/3?

Answer 1

that is a longish calculation, I can help if you tell me where you are stuck

Answer 2

well, if i recall
i got down to the expansion
but the coefficients to eachterm were alternating values (i thinnk it went rt(3)/2, 1/2, (-rt(3)/2, -1/2)

Answer 3

was on a test earlier, i just havent gotten it out of my brain

Answer 4

but i just couldnt figure a way to put those values into the series at all

Answer 5

yeah that is right.
the formula for the taylor series is T=fn(x)/n! *(x-a)^n
where fn(x) is the nth derivative

Answer 6

and the summation is missing

Answer 7

ye, that i know, but those values... the only way i could figure to put them into the series was leaving an f^n((pi)/3) in there

Answer 8

and i dnt think she wasaccepting that, otherwise *spoiler* everyone would see that loophole and pass =P

Answer 9

:) yeah I dont think that is fine.

Answer 10

exactly haha

Answer 11

wait a sec I get a pen and a paper and figure it out

Answer 12

ok, thanks. its just been bugging me like crazy

Answer 13

\[\sqrt{3}/2 \sum_{0}^{\infty}((-1)^{2n}/(2n!))*(x-\pi/3)^{2n}\]
+
\[1/2 \sum_{1}^{\infty}((-1)^{2n}/(2n+1!))*(x-\pi/3)^{2n+1}\]

Answer 14

I had two beers tonight so I might done some mistakes, but I guess it is correct. Ask if something isnt clear

Answer 15

@_@ my teacher is a troll lol. Gah she even said she expected nobody to solve it. Now I see why

Answer 16

and i do have one quick question

Answer 17

is this at high school?

Answer 18

if im not mistaken, wouldnt the (-1)^2n leave every term as positive?

Answer 19

an ye

Answer 20

high school

Answer 21

yes it would my bad, it should be just n for both

Answer 22

kinda wish the problems were harder in general so im used to them

Answer 23

buuuuuuut they have to bring iit down a bit, i guess, and im lazy -_-

Answer 24

I did not do this at high school, but I will have an exam about this in 3 weeks

Answer 25

an ok, thhanks a lot =D big help

Answer 26

my exam on ap calc ab/bc is next week. got some sample questions, not too bad

Answer 27

If you are interested in these series check the Fourier series, or ask your teacher about it. I think they are beautiful. :-)

Answer 28

will do, cuz i love all these dif things

Answer 29

just to joke around in class, ill put -e^(pi*i) in front of my answers =P

Answer 30

the taylor series only gives a good approximation about a function at a given point. The Fouries series gives for every point of the function. Also it is used a lot in life. JPEG, MP3

Answer 31

o, ok... that sounds like it could be awesome

Answer 32

one of my fav equation is e^ipi+1=0

Answer 33

has all the important bits of maths in it

Answer 34

like we were explained how taylors were often used in calculator scripts to calculate until a given tolerance was reached

Answer 35

are you living in the US?

Answer 36

an ye. im kind of self-discovering more and more about that neat little equation on my own. still need to find some proof of it or something so i canrelate it into everything else

Answer 37

an ye

Answer 38

when I graduate I might go there to teach :-)

Answer 39

o cool. where r u studying?

Answer 40

York university (UK)

Answer 41

o cool

Answer 42

math major or another?

Answer 43

also, when u teach, please do ur students a favor. intrigue the ones that carewith stuff theyve never heard of and theyll ask about it over and over an mybe even figure it out on their own

Answer 44

teacher did that with me and i basically figured out a whole chapter on my own. i was like =DDDDDDD best teacher ever

Answer 45

and that was just from mentioning one sentence about it =P so either im a huge nerd and love it or i dnt even know

Answer 46

thx for the advice, I will keep in mind.
Yes maths major

Answer 47

o cool. one other question: what is non-euclidian geometry good for/ if u kno? sounds... i dnt even

Answer 48

well I know what it is, but I dont know why is it good :)
it has interesting properties that is for sure

Answer 49

like parallel lines? mind=blown when i found out they intersected

Answer 50

if there is a given line and a point, how many parallel lines can you make from that point?

Answer 51

:DD nice one

Answer 52

it can be 0/1/2

Answer 53

hm... ok. so.... if the definition of parallel is slightly altered... im having random thoughts atm
like 4d non-flat planes an stuff. idk if those r even possible, but im tryin to think of themm

Answer 54

knowing my desired field, im probbly gonna be using some of this

Answer 55

they are in 3d

Answer 56

(physics, dream=job in researchin stuff then teachin at a university)

Answer 57

if the plane is a sphere or a ellipsoid

Answer 58

my dad is a physics teacher, but I prefer maths

Answer 59

ok. so spherical planes... ok, im starting to see how some of this might work. tho im probbly wrong =P just tying it to some things ive heard

Answer 60

but I might take some astrophysics next year

Answer 61

well, i like physics just cuz of how math-intensive it is, in addition to how some cutting edge research keeps my curiosity going constantly

Answer 62

them together=braingasm

Answer 63

dont ask a lot about these planes because I never learnt about them, just read a few things

Answer 64

nice nice :) I love mechanics

Answer 65

ah ok. well, i think its enough to keep me thinkin bout it. might look it up myself soon

Answer 66

some1 gave me a medal and became my fan, but dont know why :D

Answer 67

o nice haha.
i may, but just cuz this is the most interesting convo ive had on here =P

Answer 68

now I know why, I helped with graphing a line

Answer 69

matrices are also a really interesting topic for me. There are bits that are boring but others are really funky

Answer 70

o haha. i feel horrible when i try to help some ppl.... ill say something and then they wont get it cuz ill explain it before knoiwing their math level

Answer 71

an o. i havent dealt much with matrices. tho i need to. they just havent been stressed in any of my classes for some reason

Answer 72

well, ive gotta go finish up some homework. been great talkng, take care =D