MATH 1300 Study Guide - Quiz Guide: Binomial Theorem, Maxima And Minima

• School: CU-Boulder
• Department: Mathematics
• Course: MATH 1300
• Professor: All

Document Summary

This is a take-home quiz, due monday, february 16th at the beginning of class. Please use this as a cover page for your work: using the de nition of the derivative as limit of di erence quotients, nd the derivatives of the following. Clearly show all of your work. (a) y = x4 (use binomial theorem, (x + h)4 =?) To simplify the numerator below, we note that (x + h)4 = x4 + 4x3h + 6x2h2 + 4xh3 + h4 by the binomial theorem (fourth row of pascal"s triangle). We have y(cid:48) = lim h 0 (x + h)4 x4 h. = lim h 0 x4 + 4x3h + 6x2h2 + 4xh3 + h4 x4 h h(4x3 + 6x2h + 4xh2 + h3) h. = 4x3. (b) y = x1/3 (use di erence of cubes, ((x + h)1/3)3 (x1/3)3 =?)