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Unformatted text preview: you can differentiate. If there is more than one variable, there will be a second equation (call the constraint equation) which allows you to sub in for the extra variable(s). Sometimes there is more than one constraint equation. As with applications of derivatives, you differentiate with respect to one of the variables already in the problem (i.e. you should not need implicit differentiation). Then you find the abs max or min by testing all the critical points and end points in the original equation. 7. L’Hopital’s Rule: L’Hopital’s Rule is a way of figuring out limits that give you an indeterminate form such as If your limit is in the form 0 or 0 f x
, then L’Hopital’s Rule says lim g x xa f ' x lim g ' x xa 0
0 , , 0 ,1 , 0 , etc. . If your limit is of the form 0 , you need to rewrite it by “forcing a fraction”: f ( x) g ( x) f ( x) 1
g ( x) ln f 1 g e g ln f e If your limit is of an exponential form 1 , , etc., you need to rewrite it by: f e 0 ln f g g 8. Newton’s Method: This is a way of approximating roots of a function (like what your calculator can do). It is an iterative process, which means you keep doing the same thing ove...
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This note was uploaded on 02/24/2014 for the course MATH 1151 taught by Professor Daniel during the Fall '12 term at Ohio State.
- Fall '12