AS.110.202 Final: Practice Final Solutions Fall 2017
Document Summary
1a) notice that every time the variables x and y show up, they show up together in the same con guration. This indicates a change of variables using u = x2 + y2. Because u is a continuous function of x and y, we see that in our limit u goes to 0. This can be evaluated through a number of methods, but we opt for l"hospital"s rule (which can only be applied to one variable limits!) lim u 0 u ln(u) lim u 0 ln(u) 1b) the same technique applies to this problem with u = xyz: lim u 0 sin(u) u. **note that there are other techniques you should be familiar with that weren"t covered here. Be able to recognize secretly polar limits, aka limits of functions like x3 x2 + y2. The giveaway is the x2 + y2 on the bottom. In these instances you should switch to polar coordinates.
