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Kay [80]
3 years ago
15

Find the half range Fourier sine series of the function

Mathematics
1 answer:
worty [1.4K]3 years ago
5 0
The full range is -\pi (length 2L=2\pi), so the half range is L=\pi. The half range sine series would then be given by

f(x)=\displaystyle\sum_{n\ge1}b_n\sin\dfrac{n\pi x}L=\sum_{n\ge1}b_n\sin nx

where

b_n=\displaystyle\frac2L\int_0^Lf(x)\sin\dfrac{n\pi x}L\,\mathrm dx=\frac2\pi\int_0^\pi(\pi-x)\sin nx\,\mathrm dx

Essentially, this is the same as finding the Fourier series for the function

\begin{cases}g(x)=\begin{cases}\pi-x&\text{for }0

Integrating by parts yields

b_n=\dfrac2\pi\left(\dfrac\pi n-\dfrac{\sin n\pi}{n^2}\right)=\dfrac2n

So the half range sine series for this function is simply

f(x)=\displaystyle\sum_{n\ge1}\frac{2\sin nx}n
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Before leaving to visit Mexico, Levant traded 270 American dollars and received 3,000 Mexican pesos. When he returned from Mexic
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The amount of dollars that Mr. Levant would exchange for 100 pesos on his return is <u>$9</u>.

<h3>What is an exchange rate?</h3>

An exchange rate is a rate that is used to convert one nation's currency to another.

The exchange rate is based on the purchasing power of each nation's currency.

<h3>Data and Calculations:</h3>

Dollars before traveling to Mexico = $270

Value of Mexican pesos received for $270 = 3,000 pesos

Exchange rate = $1 = 11.11 pesos (3,000/$270)

Amount of pesos left after the trip = 100 pesos

Value of 100 pesos in dollars = <u>$9</u> (100/$11.11)

Thus, the amount of dollars that Mr. Levant would exchange for 100 pesos on his return is <u>$9</u>.

Learn more about exchange rates at brainly.com/question/2202418

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