Solve for x using the Master Product. 4x^2 + 8x + 3 = 0 Master Product: And try
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Write a recursive and explicit formula for each option.
- The Arnolds
Save a nickel on the first day of the month and then double the amount each day for a month
=> a1 =0.05
=> a2 = a1* 2 = 0.05*2
=> a3 = a2*2 = a1* 2*2
..............................................
=>recursive an =
=> explicit an = 0.05*
- The Gaineys
Start their savings by saving $10 on the first day and then $10 each day of the month
=> a1 = 10
=> a2 = a1 + 10 = 20
=> a3 = a2 +10 = 20 +10 =30
........................................................
=> recursive an =
=> explicit an = 10 + 10( n-1)
Hope it will find you well.
1.Disc method.
In this method the volume is given by:
![\boxed{V=\pi\int\limits_a^b\big[f(x)\big]^2}](https://tex.z-dn.net/?f=%5Cboxed%7BV%3D%5Cpi%5Cint%5Climits_a%5Eb%5Cbig%5Bf%28x%29%5Cbig%5D%5E2%7D)
so:
![V=\pi\int\limits_1^3x^4\,dx=\boxed{\pi\int\limits_1^3\big[x^2\big]^2\,dx}](https://tex.z-dn.net/?f=V%3D%5Cpi%5Cint%5Climits_1%5E3x%5E4%5C%2Cdx%3D%5Cboxed%7B%5Cpi%5Cint%5Climits_1%5E3%5Cbig%5Bx%5E2%5Cbig%5D%5E2%5C%2Cdx%7D)
A) Function
over the interval ![[1,3]](https://tex.z-dn.net/?f=%5B1%2C3%5D)
B) We use disk method and f(x) is function of variable x, so we <span>rotate the curve about the x-<span>axis.
2. Shell method.
In this case volume is given by:
</span></span>
So there will be:
A) Function
over the interval
B) We use shell method and f(x) is function of variable x, so we <span>rotate the curve about the y-<span>axis.</span></span>
In this method the volume is given by:
so:
A) Function
B) We use disk method and f(x) is function of variable x, so we <span>rotate the curve about the x-<span>axis.
2. Shell method.
In this case volume is given by:
</span></span>
So there will be:
A) Function
B) We use shell method and f(x) is function of variable x, so we <span>rotate the curve about the y-<span>axis.</span></span>