Economics 3364A/B Lecture Notes - Lecture 2: Budget Constraint

• School: Western University
• Department: Economics
• Course: Economics 3364A/B
• Professor: holdi

Document Summary

Solutions to quiz 5 type indeterminated form, so the l"hospital"s rule applies directly: ln(x2 + 2x) ln x lim x 0+ = 1: evaluate limx 0+ (1 sin x)3/x. Following the standard procedure, let f (x) = (1 sin x)3/x. Ln(1 sin x) = 3 ln(1 sin x) x. 0 type, hence hospital"s rule applies lim x 0+ ln f (x) = lim x 0+ Therefore, limx 0+ (1 sin x)3/x = e 3: if g (x) = sin x + 1 x2 and g( ) = 1, nd g(x). Solution: g(x) = r g (x) dx = r (sin x + x 2) dx = cos x 1/x + c. by g( ) = 1, one obtains. 1 = cos 1/ + c = 1 1/ + c from which one gets c = 1/ . Therefore, g(x) = cos x 1/x + 1/ .