4. (10 %) Sketch a graph of the region bounded by the graphs of the equations: inside the circle r = 3 cos θ and outside the cardioid r = 1 + cos θ. Then use a double integral to find the arca of the region.

(13) A logistic population model with relative growth rate 0.1 per year and carrying capacity 50 thousand can be expressed by the differential equation =0.1P(1 - ), with P in thousands and t in years. Given that the initial population is 9 thousand. Find the population size after 20 years. (If you memorized the formula, then you need to derive it for this problem.)

4. (10 %) Sketch a graph of the region bounded by the graphs of the equations: inside the circle r = 3 cos θ and outside the cardioid r = 1 + cos θ. Then use a double integral to find the arca of the region.

相關申論題

相關試卷