1. Denote L(t) the length of a fish at time t, and assume the fish grows according to the von Bertalanffy equation dL dt = k(22 − L(t)) with L(0) = 3 : (a) (2 points) Solve this differential equation. (b) (1 point) Use your solution to determine k under the assumption that L(2) = 9. Must give an exact value/expression. (c) (1 point) Find limt→[infinity] L(t). What does this describe in our real world situation. 2. (3 points) Suppose f(x) = 1 (x+2)1/3 is approximated by a third order Taylor polynomial near x = −1. Find the maximum possible error of this approximation for x ∈ [−1, 0]. Write your answer as a fraction. 3. (3 points) Find the solution to the differential equation dy dx = 3x 2 (1 + y)e y with y0 = 0 when x0 = 2