midterm2-sol - Analysis Math 325 Midterm 2 1(25 points P Let cfw_xn be a sequence and suppose that limn nxn exists and is strictly positive Prove

midterm2-sol - Analysis Math 325 Midterm 2 1(25 points...

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Analysis, Math 325Midterm 2November 20, 20171. (25 points)Let{xn}be a sequence, and suppose thatlimn→∞nxnexists and is strictly positive. Provethatn=1xnis divergent.
2. (20 points)Letf:RRbe continuous, and suppose thatf(0)>0. Prove that there exists an interval(-a, a) witha >0 on whichftakes positive values (i.e.,f(x)>0 for allx(-a, a)).

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