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: none of the above
Step-by-step explanation: when performing an hypothesis test and we want to make conclusion by comparing the p-value with the level of significance α
When p is greater than α, we reject the null hypothesis because it simply implies that we have a larger chance to commit a type 1 error ( α is the probability of committing a type 1 error an error where we reject the null hypothesis instead of accepting it ) which means we reject the null hypothesis.
When p is lesser than level of significance α, it means that we have a lesser chance of committing a type 1 error, which means we accept the null hypothesis.
Answer:
That's why I love... Nestlé Crunch, AAAHHHHH
Step-by-step explanation:
We know that
Two angles are said to be co-terminal <span>if they have the same initial side and </span>
<span>the same terminal side.
</span>
(52π/5)-----> 10.4π<span>
so
</span>(52π/5)-5*2π------> (2π/5)
the answer is
the positive angle less than one revolution around the unit circle that is co-terminal with angle of 52π/5 is 2π/5
