- #1
Lucy Yeats
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Homework Statement
Taylor's theorem can be stated f(a+x)=f(a)+xf'(a)+(1/2!)(x^2)f''(a)+...+(1/n!)(x^n)Rn
where Rn=fn(a+y), 0≤y≤x
Use this form of Taylor's theorem to find an expansion of sin(a+x) in powers of x, and show that in this case, mod([itex]\frac{x^n Rn}{n!}[/itex])[itex]\rightarrow[/itex]0 as n[itex]\rightarrow[/itex][itex]\infty[/itex] for all x.
Homework Equations
The Attempt at a Solution
sin(a+x)=sin(a)+xcos(a)-[itex]\frac{1}{2!}[/itex]x^2sin(a)-[itex]\frac{1}{3!}[/itex]x^3cos(a)...
I don't know how to prove the next bit. Also, I don't understand why Rn=fn(a+y) rather than Rn=fn(A). Any help would be great.
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