MAT137Y1 Lecture : MAT 137Y 2007-08Winter Session, Self Generated Solutions to Problem Set 6.pdf

• School: UTSG
• Department: Mathematics
• Course: MAT137Y1
• Professor: all

Document Summary

Mat 137y 2007-08 winter session, solutions to problem set 6. 1 f (cid:48)(x) = lim h 0: applying the de nition of derivative, f (x + h) f (x) = lim h 0 h h x x + x + h)( x + h) x + x + h( x + h) x h. 2x3/2: for f (x) = 5 x4 and c = 1, the difference quotient is x. = lim h 0 x x + h x + h h x x (x + h) x + h) x + h( x + = lim h 0 h x f ( 1 + h) f ( 1) h. = h3 + 4h2 6h + 4, h. 5 (h4 4h3 + 6h2 4h + 1) 4 h so f (cid:48)( 1) = lim h 0. H3 + 4h2 6h + 4 = 4: checking the one-sided limits, we have f (1 + h) f (1) h lim h 0+