I am stumped on these last parts of my hw due...
dy/dx=x^2y, f(0)=1....find f(.2)
f(0)=7, f'(0)=-4,f''(0)=1,f'''(0)=6
Find the 3rd degree Taylor polynomial and use that to approximate f(1.3)
g(x)=f(x^2)...what's the 4th degree taylor
h(x)= the integral from 0 to x of f(t)dt...find the 4th degree taylor
Can anyone help me on any of these?
This is a seperable differential equation
so
Integrating we get
So we solve for y getting
Now using the initial condition
so
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For the second one since all the values given are evaluated at zero this is a maclaurin sereis
so
Or in this case
Now to approximate
we just substitute
So assuming that converges on the interval of integration