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.
Answer:
The answer to the equation from question 7 is 14.
Step-by-step explanation:
In question 7, we are given an equation.
2³ + (8 - 5)² - 3
First, subtract 5 from 8 in the parentheses.
2³ + 3² - 3
Next, solve the exponents for 2³ and 3².
8 + 9 - 3
Add 8 to 9.
17 - 3
Subtract 3 from 17.
14
So, the answer to this equation from question 7 is 14.
Answer:
The average rate of change for the given function in the interval (-5, -1) is 0 (zero)
Step-by-step explanation:
The average rate of change of a function over an interval is the quotient between the difference between the function evaluated at the ends of the interval divided by the length of the interval. That is for our case:
the average rte of change of h(t) in the interval (-5, -1) is:

so we find:

then the average rate of change becomes:

Answer:
<h3>
Commutative property </h3>
Step-by-step explanation:
The "Commutative Laws" say: when we add we can swap numbers over and still get the same answer.
8 - 2 = (8) + (-2) = (-2) + (8) = -2 + 8