Answer:
Using either method, we obtain: 
Step-by-step explanation:
a) By evaluating the integral:
![\frac{d}{dt} \int\limits^t_0 {\sqrt[8]{u^3} } \, du](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%20%5Cint%5Climits%5Et_0%20%7B%5Csqrt%5B8%5D%7Bu%5E3%7D%20%7D%20%5C%2C%20du)
The integral itself can be evaluated by writing the root and exponent of the variable u as: ![\sqrt[8]{u^3} =u^{\frac{3}{8}](https://tex.z-dn.net/?f=%5Csqrt%5B8%5D%7Bu%5E3%7D%20%3Du%5E%7B%5Cfrac%7B3%7D%7B8%7D)
Then, an antiderivative of this is: 
which evaluated between the limits of integration gives:
and now the derivative of this expression with respect to "t" is:
b) by differentiating the integral directly: We use Part 1 of the Fundamental Theorem of Calculus which states:
"If f is continuous on [a,b] then
is continuous on [a,b], differentiable on (a,b) and 
Since this this function 
is continuous starting at zero, and differentiable on values larger than zero, then we can apply the theorem. That means:
Average speed = (distance covered in some time) / (time to cover the distance)
4 hours 45 minutes = 4-3/4 hours = 4.75 hours
Average speed = (3,800 km) / (4.75 hours) = 800 km/hr
After two weeks sasa would have bike a total of 350 miles.
The general term is obtained by starting with the initial value 5 and then subtracting 4 each time you wish to generate a new term:
a2 = second term = 5+(2-1)(-4) = 5+(-4) = 1
General term:
an = nth term = 5+(n-1)(-4)
Thus, the 21st term is 5+(21-1)(-4) = 5 + (20)(-4) = -75 (answer)
5(x - 2) + 3x = 5x - 10 + 3x = 8x - 10
