MATH214 Quiz: Quiz 1.pdf
7 Feb 2015
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Instructions: show your work, answers should be explained. Do not speak to or communicate with other students. Problem 1. (5 pt. : calculate the limit of the sequence an = en+2 sin(e n). I have a 2 liters capacity empty bottle of water. The rst day, i lled it with one liter of water. Everyday, i am allowed to add half the quantity lled the day before. For example, the second day i would add half a liter, the third day 1/4 of a liter, etc I am the only one who can add water to the bottle. After some re exion, i thought i won"t be able to ll the bottle with exactly 2 liters before i die . Answer is not written problem is not solved! 1. n en+2 sin(e n) = lim lim ables x = e n. Therefore, this sequence is convergent. e n = e2 lim x 0 n e2 sin(e n) sin(x) x.
