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MATH 1231 Lecture Notes - Lecture 3: Squeeze Theorem, Floor And Ceiling Functions

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coralbee560
5 Sep 2018
School
GWU
Department
Mathematics
Course
MATH 1231
Professor
Foroozan, F

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MATH 1231 Lecture Notes - Lecture 2: Oliver Heaviside, Asymptote

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MATH 1231 Lecture Notes - Lecture 3: Squeeze Theorem, Floor And Ceiling Functions

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Document Summary

= 50 15 + 4 = 39: lim , limit ^(cid:1865) = ^(cid:1866) (when n > 0, limit (cid:3289) = (cid:3288) (when n > 0, lim (cid:1858)(cid:4666)(cid:4667) If f is a polynomial & a rarional function and a is in the domain of f, then. Fact: if f(x) = g(x), where x a, then (cid:1812)(cid:1813) (cid:2188)(cid:4666)(cid:4667)=(cid:1812)(cid:1813) (cid:2189)(cid:4666)(cid:4667) 1 1, therefore lim (cid:2868)|| = dne (does not exist) Example: |x| = x if x 0 & -x if x < 0. [[x]] is the greatest integer that is less than or equal to x. If f(x) g(x) when x is nearby a, except possibly at a, and the lim (cid:1858)(cid:4666)(cid:4667) and lim (cid:1859)(cid:4666)(cid:4667) both exist, then lim (cid:1858)(cid:4666)(cid:4667) lim (cid:1859)(cid:4666)(cid:4667). If u(x) z(x) v(x) when x is nearby a, except possibly at a, if lim (cid:1873)(cid:4666)(cid:4667)= lim (cid:1874)(cid:4666)(cid:4667)=, then (cid:1812)(cid:1813) (cid:4666)(cid:4667)=. Limit laws cannot be applied; limit does not exist according to the graph, therefore the limit dne.

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Related Questions

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