MATH137 Lecture Notes - Lecture 9: Maxima And Minima, Derivative Test, Inflection Point

• School: University of Waterloo
• Department: Mathematics
• Course: MATH137
• Professor: Catherine Briggs

Document Summary

Math 137 week 9 notes dr. paula smith. We return to the idea of taking limits. Previously we have noticed that plugging the limit of x into f(x) may give a real number (including 0), Undefined or infinity, or such answers as 0/0, / , 0* , or . As we have seen, in the case of rational functions, it may be possible to cancel out the factors causing the difficulty. = limx a f (x) / g (x). If l"hospital"s rule results in another ratio that is indeterminate, we can do l"hospital"s rule again, until the answer is either real or. While l"hospital"s rule doesn"t work directly upon an indeterminate product, it is possible to modify a product of the form f(x)*h(x) to a ratio of the form f(x)/ (1/h(x)). L"hospital"s rule can work with limx a f(x)/ (1/h(x)) because it is an indeterminate ratio.