1. [5 marks] Consider L = lim n 6 1 -(+) i= Write down an integral with value L. Justify your expression. 2. [5 marks] Compute Jaretan (1) dr. 3. [5 marks] Compute cos x dx. [ co COS 4. [5 marks] Find a function y(x) satisfying dy + y cos x = 3 cos x, y(0) = 5. dx 5. [5 marks] Determine if the following series converges or diverges S = M8 n=1 3n 52n+1* If it converges, compute its value. If it diverges, determine if S = , S = -, or neither. 6. [5 marks] Using Simpson's method, how many intervals are required to approximate 1 dx 1+x 2 and ensure an error of at most 3(55) -? You may use the error bound for Simpson's below where f(4)(x) L: L (b-a)5 180 n4