Warm-up A rancher has 200 feet of fencing with which to enclose 2 rectangular corral (see picture). What dimensions should be used so the enclosed area will be a maximum?

23. Section 4.7 L’Hopital’s Rule

L’Hopital’s Rule EQ – When is L’Hopital’s rule used?

L’Hopital’s Rule L’Hopital (Lo-pee-tal) was french mathematician who wrote the first calculus textbook L’Hopital’s rule is used to evaluate limits of certain types of quotients of two functions If the quotient has an indeterminate form , you can replace with

Caution! You need to be careful to take derivatives of numerator and denominator separately! Do not use the quotient rule!!

Example Use L’Hopital’s rule to evaluate

Example Use L’Hopital’s rule to evaluate

Example Use L’Hopital’s rule to evaluate

Example Use L’Hopital’s rule to evaluate

Example Use L’Hopital’s rule to evaluate

Example Use L’Hopital’s rule to evaluate If you get 00, then take ln Now exponentiate (undo the ln)

Comparing Growth of Functions We say f(x) grows faster than g(x) if

Example Which grows faster? Therefore f(x)=x2 grows faster Write this as

Assignment Pg. 277: #1-19 odd, 27, 31, 43, 49, 59