Ten-thousand AFAFANDIUAHDIUAHIUDHAIDh (had to write 20 more "letters")
Answer:
0.0032
Step-by-step explanation:
We need to compute
by the help of third-degree Taylor polynomial that is expanded around at x = 0.
Given :
< e < 3
Therefore, the Taylor's Error Bound formula is given by :
, where ![$M=|F^{N+1}(x)|$](https://tex.z-dn.net/?f=%24M%3D%7CF%5E%7BN%2B1%7D%28x%29%7C%24)
![$\leq \frac{3}{(3+1)!} |-0.4|^4$](https://tex.z-dn.net/?f=%24%5Cleq%20%5Cfrac%7B3%7D%7B%283%2B1%29%21%7D%20%7C-0.4%7C%5E4%24)
![$\leq \frac{3}{24} \times (0.4)^4$](https://tex.z-dn.net/?f=%24%5Cleq%20%5Cfrac%7B3%7D%7B24%7D%20%5Ctimes%20%280.4%29%5E4%24)
![$\leq 0.0032$](https://tex.z-dn.net/?f=%24%5Cleq%200.0032%24)
Therefore, |Error| ≤ 0.0032
Answer:![43.54 ft^3/min](https://tex.z-dn.net/?f=43.54%20ft%5E3%2Fmin)
Step-by-step explanation:
Given
Thickness of oil slick=0.07 foot
radius of slick=110 ft
![\frac{\mathrm{d} r}{\mathrm{d} t}=0.9 ft/s](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20r%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D0.9%20ft%2Fs)
Let V be the volume of oil slick
so, ![V=0.07\pi \cdot r^2](https://tex.z-dn.net/?f=V%3D0.07%5Cpi%20%5Ccdot%20r%5E2)
rate of oil flowing is
![\frac{\mathrm{d} V}{\mathrm{d} t}=0.07\times 2\pi \cdot r\frac{\mathrm{d} r}{\mathrm{d} t}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20V%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D0.07%5Ctimes%202%5Cpi%20%5Ccdot%20r%5Cfrac%7B%5Cmathrm%7Bd%7D%20r%7D%7B%5Cmathrm%7Bd%7D%20t%7D)
![\frac{\mathrm{d} V}{\mathrm{d} t}=0.07\times 2\pi \times 110\times 0.9=43.54 ft^3/min](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20V%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D0.07%5Ctimes%202%5Cpi%20%5Ctimes%20110%5Ctimes%200.9%3D43.54%20ft%5E3%2Fmin)