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Math1210 Weekly Assignment 3 Spring, 2016 (Limits and continuity 1.5,1.6) instructor: Uid number: name: Instructions: Please show all of your work as partial credit will be given where appropriate, and there may be no credit given for problems where there is no work shown. All answers should be completely simplified, unless otherwise stated. No calculators or electronics of any kind are allowed. (Total of 50 points possible.) 1. (20 points) Evaluate each limit. x2 − 2x + 2 x→∞ 2x3 + 5x + 1 (a) (5 points) lim (b) (5 points) lim+ x→2 (c) (5 points) lim x→∞ 3x + 1 2−x √ x2 − 3x − 1 − cos x + sin x x→∞ x3 (d) (5 points) lim √ 2x + 5 [Hint: multiply by 1 in a clever way] 2. (15 points) State whether the indicated function is continuous at the point 1. If it is not continuous at 1, identify the type of discontinuity. (a) f (x) = (x − 1)(x + 3) (b) g(x) = |x − 1| 6 (c) h(x) = x−1 t3 − 2t2 − 5t + 6 (d) f (t) = t2 − 1 Page 2 3. (5 points) From the graph of h(x) given below, indicate the interval of definition of h(x) and the intervals on which h(x) is continuous. Indicate left or right continuity when possible. Page 3 4. (10 points) A monk decided to climb to the top of a mountain in order to reach a Buddhist temple. He started his journey at 6 AM, and he arrived at noon. The next day, he returned along the same path, starting again at 6 AM and getting to the bottom at noon. Show that there exists a point along the path where the monk stood at the exact same time on both days. [Hint: use the Intermediate Value Theorem]. Page 4