Read the problems carefully and answer the questions asked. Write neatly and indicate clearly your answer to each problem. If you need more space, use the backs of these pages and clearly indicate where the continuation may be found. You must show your work to obtain full credit. Points may be deducted if you do not justify your nal answer. Calculators, notes, books, or collaboration with others are not allowed. 3x2 3x + 4 (x 2)(x2 + 1) [24 points] determine whether or not the limit exists. If the limit exists nd it, and indicate clearly how you obtained your answer. If the limit does not exist give reasons why. (i) lim x 0 sin 3x. 5x + 7x2 (ii) (iii) lim x x e5/x 1 sin x x. Clearly explain your reasoning: [20 points] consider the curve given in polar coordinates by r = sin3( .
