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Scrat [10]
3 years ago
7

Help please ????????

Mathematics
2 answers:
julsineya [31]3 years ago
6 0

8+8+6+6+12+12

16+12+24

40+12

52

Naily [24]3 years ago
5 0

The surface area of this prism is equal

two areas of rectangular 2m × 4m + two areas of rectangular 2m × 3m + two areas of rectangular 3m × 4m

Calculate:

SA=2\cdot2\cdot4+2\cdot2\cdot3+2\cdot3\cdot4=52 m^2

Answer: 52 m²

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Now, lets evaluate the same integral using power series. first, find the power series for the function f(x = \frac{32}{x^2+4}. t
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No idea what the previous part of the problem is, but you have

f(x)=\dfrac{32}{x^2+4}=\dfrac8{1-\left(-\frac{x^2}4\right)}=\displaystyle8\sum_{n\ge0}\left(-\frac{x^2}4\right)^n
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which is valid for \left|-\dfrac{x^2}4\right|, or |x|. So the integral from 0 to 2 is

\displaystyle\int_0^2f(x)\,\mathrm dx=\int_0^28\sum_{n\ge0}\left(-\frac14\right)^nx^{2n}\,\mathrm dx
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Note that since the power series only converges on the interval if x is strictly less than 2, which means we have to treat this as an improper integral.

=\displaystyle8\sum_{n\ge0}\left(-\frac14\right)^n\lim_{t\to2^-}\int_0^tx^{2n}\,\mathrm dx[/tex]
=\displaystyle8\sum_{n\ge0}\left(-\frac14\right)^n\lim_{t\to2^-}\frac{x^{2n+1}}{2n+1}\bigg|_{x=0}^{x=t}
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