anonymous
  • anonymous
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].
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[P _{0}=0\] \[P _{1}=x\] P _{2}=x
anonymous
  • anonymous
but i am not sure how to do the bound error!!
anonymous
  • anonymous
\[x \in [-0.5,0.5].\]

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anonymous
  • anonymous
use reminder term in Lagrange form calculatded at max of your interval
anonymous
  • anonymous
i knew but i am not sure what should i put for the M \[\left| R _{n}(x) \right|=M \left| x-a \right|^{n+1}/(n+1)!\]
anonymous
  • anonymous
the value of the 4th derivative at the point 0.5
anonymous
  • anonymous
sry third, in your case
anonymous
  • anonymous
n = 0,1,2
anonymous
  • anonymous
i still don't really get it!!
anonymous
  • anonymous
ok, wait
anonymous
  • anonymous
\[P(x) = f(0) + f \prime(0)x + f \prime \prime(0)x ^{2}/2! + f \prime \prime \prime(0,5)0.5^{3}/3!\] the last term is you max error
anonymous
  • anonymous
just find the derivatives till order 3
anonymous
  • anonymous
ok now?
anonymous
  • anonymous
yea,thank you!!

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