Answer:


Step-by-step explanation:
a.
![[\because \int \dfrac{dx}{x}=\log |x|+C]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Cint%20%5Cdfrac%7Bdx%7D%7Bx%7D%3D%5Clog%20%7Cx%7C%2BC%5D)
b.
![[\because \int x^n dx=\dfrac{x^{n+1}}{n+1}+C]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Cint%20x%5En%20dx%3D%5Cdfrac%7Bx%5E%7Bn%2B1%7D%7D%7Bn%2B1%7D%2BC%5D)
c.
![[\because \dfrac{adx}{x\sqrt{x^2-a^2}}=\csc^{-1}(\dfrac{x}{a})+C]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Cdfrac%7Badx%7D%7Bx%5Csqrt%7Bx%5E2-a%5E2%7D%7D%3D%5Ccsc%5E%7B-1%7D%28%5Cdfrac%7Bx%7D%7Ba%7D%29%2BC%5D)
13.5/3 = 4.5
He hiked for 4.5 hours.
Answer:
The average rate of change is -3.
Step-by-step explanation:
We are given the function:

And we want to find the average rate of change from <em>x </em>= 0 to <em>x </em>= 3.
In other words, we will compute the function at the two endpoints, and then find the slope of the line that crosses the two points.
For our first endpoint at <em>x</em> = 0, our function evaluates to:

So, our first point is (0, 9).
For our second endpoint at <em>x</em> = 3, our function evaluates to :

So, our second point is (3, 0).
Then by the slope formula, our average rate of change will be:
