Answer:
integers, rationals, irrational, real numbers, imaginary, and complex numbers.
Answer:
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General Formulas and Concepts:
<u>Calculus</u>
Limits
Limit Rule [Variable Direct Substitution]:

Special Limit Rule [L’Hopital’s Rule]:

Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Addition/Subtraction]:
![\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28x%29%20%2B%20g%28x%29%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28x%29%5D%20%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bg%28x%29%5D)
Derivative Rule [Basic Power Rule]:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Chain Rule]:
![\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify given limit</em>.

<u>Step 2: Find Limit</u>
Let's start out by <em>directly</em> evaluating the limit:
- [Limit] Apply Limit Rule [Variable Direct Substitution]:

- Evaluate:

When we do evaluate the limit directly, we end up with an indeterminant form. We can now use L' Hopital's Rule to simply the limit:
- [Limit] Apply Limit Rule [L' Hopital's Rule]:

- [Limit] Differentiate [Derivative Rules and Properties]:

- [Limit] Apply Limit Rule [Variable Direct Substitution]:

- Evaluate:

∴ we have <em>evaluated</em> the given limit.
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Learn more about limits: brainly.com/question/27807253
Learn more about Calculus: brainly.com/question/27805589
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
He can give at most 2 adult haircuts with the remaining time
<h3>How many adult haircuts at most can he give with the remaining time? </h3>
The inequality is given as:
0.75C + 1.25A <= 7
Also, we have
C = 5
Substitute C = 5 in 0.75C + 1.25A <= 7
0.75 * 5 + 1.25A <= 7
Evaluate the product
3.75 + 1.25A <= 7
Evaluate the like terms
1.25A <= 3.25
Divide by 1.25
A <= 2.6
Rewrite as
A < 3
Hence, he can give at most 2 adult haircuts with the remaining time
Read more about inequalities at:
brainly.com/question/15010638
#SPJ1
<u>Complete question</u>
Horace is a professional hair stylist. Let C represent the number of child haircuts and A represent the number of adult haircuts that Horace can give within 7 hours. 0.75C + 1.25A <= 7
Horace gave 5 child haircuts.
How many adult haircuts at most can he give with the remaining time?
Answer:
B AND B Because they are the only awnsers that make grammatical sense.