MATH 221 Study Guide - Final Guide: Intermediate Value Theorem, Mean Value Theorem, Squeeze Theorem

• School: University of Illinois
• Department: Mathematics
• Course: MATH 221
• Professor: Jason A.Anema

Document Summary

= limx 2 ( x + 2 + 2) = 4. (2 x)( x+2+2) x+2 4: l"h opital"s rule. Can be used when you have a limit of a quotient of two functions limx a f (x) g(x) which. Remember that it can also be used on things of the form f (x)g(x), is an indeterminate form: where we rst change the function to eg(x) log f (x) and check that limx a log f (x) From here it"s usually clear than a bunch of things go to zero in the limit, and we just look at what we have left over. If f is continuous at b and limx a g(x) = b, then limx a f (g(x)) = f (limx a g(x)) = f (b). We moved the limit inside and used l"h opital to calculate limx a.