Answer:
A) 
General Formulas and Concepts:
<u>Calculus</u>
Discontinuities
- Removable (Hole)
- Jump
- Infinite (Asymptote)
Integration
- Integrals
- Definite Integrals
- Integration Constant C
- Improper Integrals
Step-by-step explanation:
Let's define our answer choices:
A)
B) 
C) 
D) None of these
We can see that we would have a infinite discontinuity if x = 2/3, as it would make the denominator 0 and we cannot divide by 0. Therefore, any interval that includes the value 2/3 would have to be rewritten and evaluated as an improper integral.
Of all the answer choices, we can see that A's bounds of integration (interval) includes x = 2/3.
∴ our answer is A.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
Answer:
The following variable is categorical.
Step-by-step explanation:
Consider the provided information.
Categorical variables: It take the values of categories or labels and position an entity in one of more classes.
Quantitative variables: It take numerical values and represent a calculation of some kind.
Now consider the given scenario.
Teenagers with a question that asks ‘‘Do you eat at least five servings a day of fruits and vegetables?"
Here we have two categories i.e fruits and vegetables.
Therefore, the following variable is categorical.
Rita spent 20$. By multiplying 5 pairs with 4$ we can see that it will equal 20$
Answer:
8x+4 and 10x+4
Step-by-step explanation:
Using the distributive property, you times 8 by x and then 8 by one half: 8x & 8*1/2. 8x+4
You then do the same for 10(x+2/5): 10x and then 10 divided by 5 and times by 2. This leaves you with 10x+4.
I hope this helped. :)
<h3>
Answer: g(x) = (-2/3)x^2</h3>
=====================================================
Explanation:
The blue parent function has a positive coefficient of 1. The purple g(x) function is a reflection of f(x) over the x axis, so everything is now negative. The coefficient must be negative as well.
But the answer is simply not g(x) = -x^2 because plugging x = 3 does not lead to y = -6 as the point (3,-6) shows.
Let's say the coefficient is k for now. So we have y = kx^2
Plug in x = 3 and y = -6. Solve for k
y = kx^2
-6 = k(3)^2
-6 = k*9
9k = -6
k = -6/9
k = -2/3
So we update y = kx^2 into y = (-2/3)x^2
Meaning that g(x) = (-2/3)x^2 is the equation of the purple curve.
Plug x = 3 into g(x) to find that
g(x) = (-2/3)x^2
g(3) = (-2/3)(3)^2
g(3) = (-2/3)(9)
g(3) = -6
which is the output we want, so this confirms we have the correct coefficient.
