Question

infinite differentiable function

Answer 1

f(0) = 1, f'(0) = 0.1, f''(0) = 0.01, f'''(0) = 0.001, etc
Find f(10) to five decimal places

Answer 2

i want to say its a cosine function

Answer 3

http://www.math.smith.edu/~rhaas/m114-00/chp4taylor.pdf
is this something like what you're trying to do?

Answer 4

yes i think so

Answer 5

Yeah, use taylor's series here, do you know how to set up the equation?

Answer 6

no i am learning this stuff...i need explanation if you can

Answer 7

Yeah, sure

Answer 8

@ash2326 i though you were helping me but never mind i got it

Answer 9

@heyheyhelpme did you reply to my question? I never got a notification

Answer 10

my question duhhhhh

Answer 11

so am i suppose to use this formula?
f(x) = f(x) ≈ P2(x) = f(a)+ f'(a)(x −a)+f''(a)/2(x −a)^2

Answer 12

Yes, this is the Taylor's series around x=0, also call Maclaurin's Series,
\[f(x)\sim f(0)+f'(0)\times x+f''(0) \frac{x^2}{2!}+f'''(0) \frac{x^3}{3!}\]

Answer 13

Now plugin these values and find f(x),
can you do that?

Answer 14

\[1 + 0.1x + ((0.01x^2)/2!) + (0.001x^3)/3!\]

Answer 15

am i right?

Answer 16

\[f(x)\sim f(0)+f'(0)\times x+f''(0) \frac{x^2}{2!}+f'''(0) \frac{x^3}{3!}\]
\[f(x)=1+0.1x+0.01 x^2/2+0.001 x^2/3!\]
There was a small mistake

Answer 17

oh so the 2 won't be factorial

Answer 18

2!=2

Answer 19

ugh ya....i totally forgot tht

Answer 20

No problem, now you need to put x=10 and you'll get f(10)

Answer 21

now just plugin 10?

Answer 22

oh ya thats easy thanks

Answer 23

Welcome Sir :D

Answer 24

so the answer is 2.6667

Answer 25

correct:)

Answer 26

i did this much complicated sum to get that small answer? calculus your kiddin me

Answer 27

Find f(10) to five decimal places

2.6667

That's only four d.p.s, you probably need the next term in the taylor series.
\[\Large f(x)\sim f(0)+f'(0)\times x+f''(0) \frac{x^2}{2!}+f'''(0) \frac{x^3}{3!} + f''''(0) \frac{x^4}{4!}\]

Answer 28

f'(0) = 0.1, f''(0) = 0.01, f'''(0) = 0.001 so f''''(0) = 0.0001