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The instructions and problems for exam 1 of math 115. The exam covers topics such as functions, sequences, and series. Students are prohibited from wearing hats or sunglasses, using cell phones, or bringing book bags into the exam room. The exam consists of questions related to finding the domain of a function, identifying arithmetic and geometric sequences, and evaluating series. The document also includes instructions for handing in the exam and information about the exam format.
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โ (^39) โ x 2 x^2 โx + 2. (a) State the domain of f (x) using set notation.
(b) State the domain of f (x) using interval notation.
(a) (3pts) Suppose an is an arithmetic sequence such that lim nโโ an = a 1. What do you know about the common difference d? Briefly explain your answer.
(b) (3pts) Suppose an is a geometric sequence such that (^) nlimโโ an = 0. What do you know about the common ratio r? Briefly explain your answer.
(a) (4pts) 4 + 4
(b) (4pts) 4 + 1 + (โ2) + (โ5) +... + (โ35)
(c) (2pts) Write the series in (b) using sigma notation.
i=
(i^2 โ 2 i) as an explicit sum and evaluate (by fully sim-
plifying) the sum.
(a) (3pts) 9999 + 9998 + 9997 + 9996 +...