MTH 171 Lecture Notes - Lecture 24: Indeterminate Form
Document Summary
Provide a generalization to each of the key terms listed in this section. The following shows that you can get one of two general cases for any real number being either a or even a = : lim g (x)(cid:21) = x a(cid:20) f (x) g (x)(cid:21) = x a(cid:20) f (x) lim. Generally, this can be known as being in indeterminate form and one good method to solve these kind of limits can be with using the squeeze theorem. If that is the case, then the following limit would con rm: f (x) h(x) g(x) Since the previous is noted, then the following would be noted: lim x c. [g (x)] a c b lim x c. L"hospital"s rule example limx 0 (cid:0)csc (x) 1 x(cid:1) x(cid:17) = limx 0(cid:16) 1 sin(x) 1 x sin(x)(cid:17) x sin(x) sin(x) x. = limx 0h d dx (x) d dx (x)sin(x)+ d d dx (sin(x)) dx (sin(x))xi.
