MAT 1322 Study Guide - Antiderivative, Telescoping Series, Ibm System P
8 Oct 2014
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Solutions: (i) [5 points] calculate lim n ln(n2 n) ln(n) page 2 of 7. Solution: this is an indeterminate form of type . This gives l"hospital"s rule to the function f (x) = ln(x2 x) ln(x) To determine the limit, we apply lim x ln(x2 x) ln(x) = lim x d dx ln(x2 x) d dx ln(x) To calculate the last limit, we could apply l"hospital"s rule again, but it is simpler to divide numerator and denominator by x2: lim x . = 2 . (alternately, one could recall that the horizontal asymptote of a rational function with equal degree on numerator and denominator is given by the ratio of the leading coe cients. ) [5 points] determine the reduced fraction p/q (with q > 0) with decimal expansion. The series in parentheses is a geometric series with initial term a = 78/1000 and common ratio r = 1/100.
