Problem 1: (4 pts) Find the slope of the line tangent to the following parameterized curve at the point when t = 1 X = ; 3 t + 1 ' y = sin(7 . t), Osts 3 Problem 2: Determine if the following sequences converge or diverge. If it converges, find the limit of the sequence. (Again, this is a sequence, not a series) In(2 n) a) an = In(n+1)' for n = 2, 3, ... (4 pts) b) ak = (K+3)2 k (4 pts) Problem 3: (4 pts) Write the following geometric series in sigma notation. Then find the value of the series or, if the series diverges, explain why it diverges. 20 40 15 -10 +- 3 9 Problem 4: (4 pts) For the following telescoping series, find a formula for the nth term of the sequence of partial sums {S,). Then evaluate lim,->co (Sn) to obtain the value of the series or, if the series diverges, explain why. 6 (5 k - 1) (5 k +4) Problem 5: (4 pts) Use the Integral Test to determine if the following series converges or diverges. Remember to check that the conditions of the test are satisfied. In (k) * 2