1. Find the area of the region between two curves below.
2. Find the area of the region between two curves below. (Hint: the answer is not 0)
3. Find the area of the region between two curves below.
5. Similar to finding the area bounded by two functions, you can also find the volume bounded by two functions and rotating its area about the x-axis. Assume f(x) represents one function and g(x) represents the other and that f(x) is greater than g(x). Then you find the volume by integrating the following:
Find the area bounded by the two functions below, between x = 0 and x = 1.
1. Evaluate the derivative below.
2. By applying implicit differentiation, find y'(x) below.
3. Assume a rectangular flower garden (see figure below) with an area of 32 ft2 is surrounded by a grass border that is 1 ft wide on two sides and 2 ft wide on the other two sides. What dimensions of the garden minimize the combined area of the garden and borders?
4. Find the critical points of the function below. Categorize them as either absolute or local extrema.
5. Assume that the initial (at t = 0) population of a prairie dog community is P(0) = 55 dogs. The community population grows at the rate of P'(t) = 20-t/5 for 0 ≤ t ≤ 200 months. Calculate the population 10 months later (including the initial count).
6. Find the area bound by two function below. Show your work.