Read before you begin: (1) this exam contains 13 problems for a total of 125 points. There are 11 pages including the cover sheet. You are responsible for checking that they are all present. (1) you must show all work to completely justify your answers in order to receive any credit. Unsupported answers will receive little or no credit. (2) you may use only the methods discussed in this class to solve the problems. (3) no calculators, cell phones, ipods, etc. (4) good luck! 125: find the following limits, if they exist. If the limit equals 00 or -00, say which it equals, and explain why very carefully. You may not use l"hospital"s rule for this problem. lim x->-3+ x+2 x 2(x + 3) sin 4x b) 1im - x->o sin 5x. You may use any methods that we have learned in this class: lim ~ x->l sin 7rx b)
