Answer: lim as x → -5 of f(x) and g(x) = 300
Domain of f(x) and g(x) is All Real Numbers
f(-5) = 200
g(-5) = 300
<u>Step-by-step explanation:</u>
The limit of f(x) as x approaches -5:
![f(x) =\dfrac{4x^3+500}{x+5}\\\\\\.\qquad =\dfrac{4(x^3+125)}{x+5}\\\\\\.\qquad =\dfrac{4(x^3+5^3)}{x+5}\qquad \text{we can factor the cubic}\\\\\\.\qquad =\dfrac{4(x+5)(x^2-5x+25)}{x+5}\\\\\\.\qquad =4(x^2-5x+25)\\\\\\\text{as x approaches -5, f(x) = }4[(-5)^2-5(-5)+25]\\\\.\qquad \qquad \qquad \qquad \qquad =4(25 + 25 + 25)\\\\.\qquad \qquad \qquad \qquad \qquad =4(75)\\\\.\qquad \qquad \qquad \qquad \qquad =300](https://tex.z-dn.net/?f=f%28x%29%20%3D%5Cdfrac%7B4x%5E3%2B500%7D%7Bx%2B5%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%3D%5Cdfrac%7B4%28x%5E3%2B125%29%7D%7Bx%2B5%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%3D%5Cdfrac%7B4%28x%5E3%2B5%5E3%29%7D%7Bx%2B5%7D%5Cqquad%20%5Ctext%7Bwe%20can%20factor%20the%20cubic%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%3D%5Cdfrac%7B4%28x%2B5%29%28x%5E2-5x%2B25%29%7D%7Bx%2B5%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%3D4%28x%5E2-5x%2B25%29%5C%5C%5C%5C%5C%5C%5Ctext%7Bas%20x%20approaches%20-5%2C%20f%28x%29%20%3D%20%7D4%5B%28-5%29%5E2-5%28-5%29%2B25%5D%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D4%2825%20%2B%2025%20%2B%2025%29%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D4%2875%29%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D300)
The limit of g(x) as x approaches -5:
g(x) = 4x² - 20x + 100
= 4(-5)² - 20(-5) + 100
= 100 + 100 + 100
= 300
There is a restriction at x = -5 for f(x), however, that discontinuity has been filled with the 200 at x = -5. So the domain is ALL REAL NUMBERs.
There are no restrictions on x for g(x) so the domain is ALL REAL NUMBERs.
Answer: 8
Step-by-step explanation:
The two parallel bars mean absolute value meaning the positive value of that number. The positive value of -8 is 8. Note that positive number in an absolute value bars reamin the same.
More examples: |9|=9
Have a nice day! :D
Hi,
Let Sydney's age be x.
Devaughn=(x-15)
x+(x-15)=37
x+x-15=37
2x-15=37
2x=37+15
2x=52
x=52/2
x=26
Sydney is 26 years old.
Hope this Helps you.
The remainder from the division of the algebraic equation is -53/8.
<h3>What is the remainder of the algebraic expression?</h3>
The remainder of the algebraic expression can be determined by using the long division method.
Given that:
where:
Using the long division method, we have:
Therefore, we can conclude that the remainder is -53/8.
Learn more about the division of algebraic equations here:
brainly.com/question/4541471
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The first reaction represented is a decomposition reaction due to the fact the bonded pair are being split apart.
The second equation is a single displacement because the B and C have switched places, which is the only change making it a single displacement. If there had been another bond and A had also moved, it would be double.
