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:
Step-by-step explanation:
This is simple: we need to only do 2 steps
1) Convert to feet
2) Get the area
1) Converting to feet is just
(ignore the use of this it's just to show the differnt things to multiply
Now we have a length of 21 and a width of 12 FEET.
2) To solve for the area, we need to multiply both dimensions.
So the answer is 252^2 FEET (DONT FORGET THE UNIT SQUARE FEET)
Step-by-step explanation:
Hence, the 55th term of the sequence is 161.
Answer:
10.5.
Step-by-step explanation:
By similar triangles:
IJ / 21 = 8 /(8+8) = 1/2
IJ / 21 = 1/2
IJ = 1/2 * 21
= 10.5.
