MATH 1A Final: math1A-fa2009-final-Christ-soln
Document Summary
Mathematics 1a, fall 2009 m. christ final examination solutions. They were very similar, so solutions are given here. 1 cos(x) ln(x) 1 x . dx xcos(x). (here x > 0. ) 2 (3 + ln(ln(x))) 1/2 dxp3 + ln(ln(x)). = limx /2 sin(x) for only one version. (1) calculate the following. (1a) the equation of the line tangent to f (x) = x + ex at x = 2. Solution. y = (2 + e2) + e2(x 2). (cid:3) (1b) d (1c) limx /2 rule. (1d) d. = d cos(x)x 1)xcos(x). (1e) r d constant. (1f ) d dx ecos(x) ln(x) = ( sin(x) ln(x) + cos(x)x 1)ecos(x) ln(x) = ( sin(x) ln(x) + dxp| sin(x) + cos(x)| dx. Solution. p| sin(x) + cos(x)|+c where c is an arbitrary dx r sin(2x) arcsin(t) dt. If 2x is in the range [ /2, /2], then this can be simpli ed, since then arcsin(sin(2x)) =
