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Today's calculation of Integral 387

Source: National Defence Medical College entrance exam 2008/11/02

November 5, 2008
calculusintegrationlogarithmsgeometrylimitcalculus computations

Problem Statement

Let l1, l2 l_1,\ l_2 be the tangent and nomal line respectively at the point (p,\ \ln (p \plus{} 1)) on the curve C: y \equal{} \ln (x \plus{} 1). Denote by T_i\ (i \equal{} 1,\ 2) the areas bounded by l_i\ (i \equal{} 1,\ 2), C and the y y axis respectively. Find the limit lim⁡p→0T2T1 \lim_{p\rightarrow 0} \frac {T_2}{T_1}.
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