Answer:
See the image for solution
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Answer:
Constant Volume Forced Air system
Explanation:
By applying the concepts of differential and derivative, the differential for y = (1/x) · sin 2x and evaluated at x = π and dx = 0.25 is equal to 1/2π.
<h3>How to determine the differential of a one-variable function</h3>
Differentials represent the <em>instantaneous</em> change of a variable. As the given function has only one variable, the differential can be found by using <em>ordinary</em> derivatives. It follows:
dy = y'(x) · dx (1)
If we know that y = (1/x) · sin 2x, x = π and dx = 0.25, then the differential to be evaluated is:
![y' = -\frac{1}{x^{2}}\cdot \sin 2x + \frac{2}{x}\cdot \cos 2x](https://tex.z-dn.net/?f=y%27%20%3D%20-%5Cfrac%7B1%7D%7Bx%5E%7B2%7D%7D%5Ccdot%20%5Csin%202x%20%2B%20%5Cfrac%7B2%7D%7Bx%7D%5Ccdot%20%5Ccos%202x)
![y' = \frac{2\cdot x \cdot \cos 2x - \sin 2x}{x^{2}}](https://tex.z-dn.net/?f=y%27%20%3D%20%5Cfrac%7B2%5Ccdot%20x%20%5Ccdot%20%5Ccos%202x%20-%20%5Csin%202x%7D%7Bx%5E%7B2%7D%7D)
![dy = \left(\frac{2\cdot x \cdot \cos 2x - \sin 2x}{x^{2}} \right)\cdot dx](https://tex.z-dn.net/?f=dy%20%3D%20%5Cleft%28%5Cfrac%7B2%5Ccdot%20x%20%5Ccdot%20%5Ccos%202x%20-%20%5Csin%202x%7D%7Bx%5E%7B2%7D%7D%20%5Cright%29%5Ccdot%20dx)
![dy = \left(\frac{2\pi \cdot \cos 2\pi -\sin 2\pi}{\pi^{2}} \right)\cdot (0.25)](https://tex.z-dn.net/?f=dy%20%3D%20%5Cleft%28%5Cfrac%7B2%5Cpi%20%5Ccdot%20%5Ccos%202%5Cpi%20-%5Csin%202%5Cpi%7D%7B%5Cpi%5E%7B2%7D%7D%20%5Cright%29%5Ccdot%20%280.25%29)
![dy = \frac{1}{2\pi}](https://tex.z-dn.net/?f=dy%20%3D%20%5Cfrac%7B1%7D%7B2%5Cpi%7D)
By applying the concepts of differential and derivative, the differential for y = (1/x) · sin 2x and evaluated at x = π and dx = 0.25 is equal to 1/2π.
To learn more on differentials: brainly.com/question/24062595
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