Answer:
A) added to both sides of the equation
Step-by-step explanation:
The trick here is to use an appropriate substitution. Let u=a^3.
Then du/da=3a^2, and du=3a^2da.
We can now make two key substitutions: In (3a^2)da/(1+a^6), replace 3a^2 by du and a^6 by u^2.
Then we have the integral of du/(1+u^2).
Integrating, we get arctan u + c. Substituting a^3 for u, the final result (the integral in question) is arctan a^3 + c.
Check this by differentiation. if you find the derivative with respect to a of arctan a^3 + c, you MUST obtain the result 3a^2/(1+a^6).
The graph has domain x ∈ ( 0 , +∞ )
It is first increasing and then decreasing. It has a local minimum and a global maximum.
- x^4 + x³ + 7 x² - x - 6 = ( x - 1 ) ( x + 1 ) ( x + 2 ) ( 3 - x )
The company will break even when P ( x ) = 0
The zeroes are: x 1 = 1, x 2 = 3
The company has a profit when: x ∈ ( 1, 3 )
Answer:
Option B.
Step-by-step explanation:
Slope of the line AC = ![\frac{\text{Rise}}{\text{Run}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BRise%7D%7D%7B%5Ctext%7BRun%7D%7D)
= ![\frac{\text{AB}}{\text{BC}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BAB%7D%7D%7B%5Ctext%7BBC%7D%7D)
= ![\frac{4}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B6%7D)
= ![\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D)
Slope of the line CE = ![\frac{\text{DC}}{\text{DE}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BDC%7D%7D%7B%5Ctext%7BDE%7D%7D)
= ![\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D)
Therefore, slope of the line AC = Slope of the line AC
And this is because ratio of change in y-values of the endpoints to the change in x-values of the endpoints is the same for AC as for CE.
Option B. is the answer.