Question

Calculus Help!!
Find the Taylor polynomials centred at 0 for n = 0,1,2 for the function f(x) = arcsin(x).
Find a bound on the error for each of these on the interval x\[\in\] [-0.5,0.5].

Answer 1

\[P _{0}=0\]
\[P _{1}=x\]
P _{2}=x

Answer 2

but i am not sure how to do the bound error!!

Answer 3

\[x \in [-0.5,0.5].\]

Answer 4

use reminder term in Lagrange form calculatded at max of your interval

Answer 5

i knew but i am not sure what should i put for the M
\[\left| R _{n}(x) \right|=M \left| x-a \right|^{n+1}/(n+1)!\]

Answer 6

the value of the 4th derivative at the point 0.5

Answer 7

sry third, in your case

Answer 8

n = 0,1,2

Answer 9

i still don't really get it!!

Answer 10

ok, wait

Answer 11

\[P(x) = f(0) + f \prime(0)x + f \prime \prime(0)x ^{2}/2! + f \prime \prime \prime(0,5)0.5^{3}/3!\]
the last term is you max error

Answer 12

just find the derivatives till order 3

Answer 13

ok now?

Answer 14

yea,thank you!!