2.8.1

By definition of the derivative,

We have

and

Combine these fractions into one with a common denominator:

Rationalize the numerator by multiplying uniformly by the conjugate of the numerator, and simplify the result:

Now divide this by <em>h</em> and take the limit as <em>h</em> approaches 0 :

3.1.1.
![f(x) = 4x^5 - \dfrac1{4x^2} + \sqrt[3]{x} - \pi^2 + 10e^3](https://tex.z-dn.net/?f=f%28x%29%20%3D%204x%5E5%20-%20%5Cdfrac1%7B4x%5E2%7D%20%2B%20%5Csqrt%5B3%5D%7Bx%7D%20-%20%5Cpi%5E2%20%2B%2010e%5E3)
Differentiate one term at a time:
• power rule


![\left(\sqrt[3]{x}\right)' = \left(x^{1/3}\right)' = \dfrac13 x^{-2/3} = \dfrac1{3x^{2/3}}](https://tex.z-dn.net/?f=%5Cleft%28%5Csqrt%5B3%5D%7Bx%7D%5Cright%29%27%20%3D%20%5Cleft%28x%5E%7B1%2F3%7D%5Cright%29%27%20%3D%20%5Cdfrac13%20x%5E%7B-2%2F3%7D%20%3D%20%5Cdfrac1%7B3x%5E%7B2%2F3%7D%7D)
The last two terms are constant, so their derivatives are both zero.
So you end up with

I think you just have to add all of the totals up??
Answer:
BHF
Step-by-step explanation:
Definition of inscribed
Detailed Answers:
Volume of a Sphere (V) = 4/3 πr^3
1. Diameter (d) = 21.6 cm
Radius (r) = 21.6/2 = 10.8 cm
Therefore,
= 4/3 πr^3
= 4/3 * 22/7 * (10.8)^3
= 4/3 * 22/7 * 1259.712
= 88/21 * 1259.712
=> 5278.79
Volume (V) = 5278.79 cm^3
2. Diameter (d) = 16 cm
Radius (r) = 16/2 = 8 cm
Therefore,
= 4/3 πr^3
= 4/3 * 22/7 * (8)^3
= 4/3 * 22/7 * 512
= 88/21 * 512
=> 2145.52
Volume (V) = 2145.52 cm^3
3. Diameter (d) = 24 cm
Radius (r) = 24/2 = 12 cm
Therefore,
= 4/3 πr^3
= 4/3 * 22/7 * (12)^3
= 4/3 * 22/7 * 1728
= 88/21 * 1728
=> 7241.14
Volume (V) = 7241.14 cm^3
4. Diameter (d) = 6 cm
Radius (r) = 6/2 = 3 cm
Therefore,
= 4/3 πr^3
= 4/3 * 22/7 * (3)^3
= 4/3 * 22/7 * 27
= 88/21 * 27
=> 113.14
Volume (V) = 113.14 cm^3