Answer:

General Formulas and Concepts:
<u>Calculus</u>
Limits
Limit Rule [Variable Direct Substitution]: 
Limit Rule [Variable Direct Substitution Exponential]: 
Limit Property [Multiplied Constant]: 
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>

<u>Step 2: Solve</u>
- Rewrite [Limit Property - Multiplied Constant]:
![\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4} \lim_{x \to 0} [f(x)]^4](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B1%7D%7B4%7D%5Bf%28x%29%5D%5E4%20%3D%20%5Cfrac%7B1%7D%7B4%7D%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Bf%28x%29%5D%5E4)
- Evaluate limit [Limit Rule - Variable Direct Substitution Exponential]:
![\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4}(4^4)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B1%7D%7B4%7D%5Bf%28x%29%5D%5E4%20%3D%20%5Cfrac%7B1%7D%7B4%7D%284%5E4%29)
- Simplify:
![\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = 64](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B1%7D%7B4%7D%5Bf%28x%29%5D%5E4%20%3D%2064)
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Book: College Calculus 10e
Answer:
0.18
Step-by-step explanation:
Answer:
below
Step-by-step explanation:
steps are shown above
Answer: 120 ways
Step-by-step explanation: In this problem, we're asked how many ways can 5 people be arranged in a line.
Let's start by drawing 5 blanks to represent the 5 different positions in the line.
Now, we know that 5 different people can fill the spot in the first position. However, once the first position is filled, only 4 people can fill the second spot and once the second spot is filled, only 3 people can fill the third spot and so on. So we have <u>5</u> <u>4</u> <u>3</u> <u>2</u> <u>1</u>.
Now, based on the counting principle, there are 5 x 4 x 3 x 2 x 1 ways for all 5 spots to be filled.
5 x 4 is 20, 20 x 3 is 60, 60 x 2 is 120, and 120 x 1 is 120.
So there are 120 ways for all 5 spots to be filled which means that there are 120 ways that 5 people can be arranged in a line.
I have also shown my work on the whiteboard in the image attached.
<h3>
Answer: D) 31</h3>
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Explanation:
The expression g(f(2)) has f(2) as the inner function.
Let's compute f(2)
This means we plug x = 2 into the f(x) function
f(x) = 4x^3 - 10
f(x) = 4(x)^3 - 10
f(2) = 4(2)^3-10
f(2) = 4*8-10
f(2) = 32-10
f(2) = 22
Now we'll plug this into the g(x) function
This is because g(f(2)) = g(22). I've replaced f(2) with 22
So,
g(x) = (3x-4)/2
g(22) = (3*22-4)/2
g(22) = (66-4)/2
g(22) = 62/2
g(22) = 31
Therefore, g(f(2)) = 31