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Gala2k [10]
3 years ago
11

Find the taylor polynomial t3(x) for the function f centered at the number

Mathematics
1 answer:
Vlad [161]3 years ago
5 0
e^{-3x}=\displaystyle\sum_{n=0}^\infty\frac{(-3x)^n}{n!}=1-3x+9x^2+\cdots
\sin2x=\displaystyle\sum_{n=0}^\infty\frac{(-1)^n(2x)^{2n+1}}{(2n+1)!}=2x-\dfrac{4x^3}3+\cdots

e^{-3x}\sin2x=\left(1-3x+9x^2+\cdots\right)\left(2x-\dfrac{4x^3}3+\cdots\right)
\approx T_3(x)=(1-3x+9x^2)\left(2x-\dfrac{4x^3}3\right)
T_3(x)=2x-6x^2+\left(18-\dfrac43\right)x^3
T_3(x)=2x-6x^2+\dfrac{50}3x^3
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