004 (che) (cive: dunbar, girelli (geoe/enve) e. dupont (me, beltaos. Instructions: write your name, email, id and section number at the top of this page, answer the questions in the spaces provided. There are questions on both sides of the page. There is a blank page at the end of the exam for rough work: show all work required to obtain your answers for full credit. 1. (a) di erentiate r(x) = x20 + 14. 1 + x4 : (continued) (c) di erentiate h(x) =(cid:82) x. [3] (d) calculate the limit lim x 0+ xtan(x). Nd the limit of ln(y) rst: lim x 0+ ln(y) = lim x 0+ tan(x) ln(x) We realize this is a 0 type limit, which we can"t work with. We convert it to a 0/0 type limit as follows: lim x 0+ ln(x) ( cos(x) sin(x) ) We now apply l"hospital"s rule to get lim x 0+
