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- 2. If jk is the rate of simple interest for the k-th period of time, where k = 1, 2,..., n, show that the amount of interest earned from time 0 to time n is j₁ + 2 + +Jn, if an investment of 1 is made at time 0.3. For r = 3.2 and r = 3.5, calculate the first 100 sequence values. Generate a cobweb diagram for each iterative process. (Several free applets are available online that generate cobweb diagrams for the logistic map.) What is the long-term behavior in each of these cases?3. A particle moving along the x-axis has velocity function v(t) = t²e-t. How far does the particle travel from time t = 0 to t = 5? 4. Consider the sequence {Inn {" n In-1 (a) Write out the first five terms of the sequence (b) Determine whether the sequence converges and if so find its limit