MATH 1M03 Midterm: MATH 1M03, Term Test 2

• School: McMaster University
• Department: Mathematics
• Course: MATH 1M03
• Professor: All

Document Summary

Calculus for business, humanities and the social sciences. Present value of an income stream 31. Present value of a continuous cash flow 33. Functions of more than 1 variable 46. Recap: we had a very short list of integrals that we knew also: Idea is to replace some expression in there with a "(cid:1873)" in order to get a simpler integral in (cid:1873). The key thing however is that we need (cid:1856)(cid:1873) Example: find (cid:1858)(cid:4666)(cid:1876)(cid:4667) if (cid:1858) (cid:4666)(cid:1876)(cid:4667)=(cid:4666)ln(cid:4667)(cid:3121) (cid:1858)(cid:4666)(cid:1876)(cid:4667)= (cid:4666)ln(cid:1876)(cid:4667)(cid:2873)(cid:1876) fails bacause cannot (cid:1873) or (cid:1856)(cid:1873) (cid:1873)(cid:2873)(cid:1856)(cid:1873)=(cid:1873)(cid:2874)(cid:888)+(cid:1829)=(cid:4666)ln(cid:1876)(cid:4667)(cid:2874)(cid:888) +(cid:1829) (cid:1858)(cid:4666)(cid:1876)(cid:4667)=(cid:4666)ln(cid:1876)(cid:4667)(cid:2874)(cid:888) +(cid:1829) (cid:1858)(cid:4666)(cid:1857)(cid:4667)=(cid:4666)ln(cid:1857)(cid:4667)(cid:2874)(cid:888) +(cid:1829)=(cid:882) (cid:4666)(cid:883)(cid:4667)(cid:2874)(cid:888) +(cid:1829)=(cid:882) (cid:1829)= (cid:883)(cid:888) (cid:1858)(cid:4666)(cid:1876)(cid:4667)=(cid:4666)ln(cid:1876)(cid:4667)(cid:2874)(cid:888) (cid:883)(cid:888) Replace something with (cid:1873) and replace (cid:1873) (cid:1856)(cid:1876) with (cid:1873). * when looking for (cid:1873) (cid:1856)(cid:1876), don"t worry about multiplicative constant. * recall that the techniques origins are from the chain rule, so look for chain rule idea with (cid:1873) * not on the list being the insides. * go straight to the toughest part of your integral.