Use a power series to approximate the value of the integral with an error of less than 0.0001. (Round your answer to four décimal place sin(x) dx

A jungle has 400 monkeys, and it is estimated that the maximum population of the monkeys in the jungle is 10,000. The number of monkeys tripled in the first year. Write a differential equation that describes the population of monkeys in the jungle. Solve your differential equation to find the number of monkeys in the jungle as a function of time. When will the number of monkeys reach 5,000? When is the number of monkeys growing the fastest. Describe the method you used and show all work.

In the last part, wouldn't the range be calculated by the integral change due to the two substitutions to int from 0 to pi/3?

If V=R\power{3}, and W\index{1} is the xy plane and let W\index{2} is yz-plane:     W\index{1}={(x,y,0):x,y∈R}     W\index{2}={(0,y,z):y,z∈R} then V is not the direct sum of W\index{1} and W\index{2}.