MAT133Y1 Lecture : L'Hopital's Rule.pdf
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MAT133Y1 Full Course Notes
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What do we mean when we say that 1/0 = or is in nite or does not exist. We call this a 0/0 form. ex 1 x lim x 0. = 1 (x + 2) 1 (x + 6) 1. There is a useful procedure known as l"h opital"s rule. If limx a f(x) = 0 and limx a g(x) = 0 and f0(x) g0(x) lim x a. = l then as well. lim x a f(x) g(x) = l (there are additional assumptions on f and g, but these are commonly satis ed by the functions we deal with in this course, so we shall skip the details. ) In other words, if you are trying to evaluate limx a f(x)/g(x) and it is of the form. If you get an answer, the same answer will work for limx a f(x)/g(x). In our examples, ex 1 x ex 1 is in 0/0 form at x = 0.
