Step-by-step explanation:
why would you joke I was willing to help you hun but enjoy the rest of your day
For this case we have by definition, that the volume of a sphere is given by:

Where:
r: It is the radius of the sphere
If the radius is divided by 3 we have:


ANswer:
the volume decreases considerably because the denominator increases
Answer:
2 x 10 x 4 + (4 + 10) x 2 x 6 = 80 + 168 = 248
. The series is divergent. To see this, first observe that the series ∑ 1/kn for n = 1 to ∞ is divergent for any integer k ≥ 2.
Now, if we pick a large integer for k, say k > 100, then for nearly all integers n it will be true that 1 > cos(n) > 1/k. Therefore, since ∑ 1/kn is divergent, ∑ cos(n)/n must also be divergent The *summation* is divergent, but the individual terms converge to the number 0.<span>by comparison test since cosn/n <= 1/n is convergent
and 1/n is divergent by harmonic series
so the series is conditionally converget </span>
Answer:

Domain: All Real Numbers
General Formulas and Concepts:
<u>Algebra I</u>
- Domain is the set of x-values that can be inputted into function f(x)
<u>Calculus</u>
The derivative of a constant is equal to 0
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Chain Rule: ![\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Derivative: ![\frac{d}{dx} [ln(u)] = \frac{u'}{u}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bln%28u%29%5D%20%3D%20%5Cfrac%7Bu%27%7D%7Bu%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = ln(2x² + 1)
<u>Step 2: Differentiate</u>
- Derivative ln(u) [Chain Rule/Basic Power]:

- Simplify:

- Multiply:

<u>Step 3: Domain</u>
We know that we would have issues in the denominator when we have a rational expression. However, we can see that the denominator would never equal 0.
Therefore, our domain would be all real numbers.
We can also graph the differential function to analyze the domain.