The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.

Home Continuous Functions Limits Limit Rules
See also: Theorem 2: 
del.icio.us Reddit Facebook StumbleUpon MySpace Twitter Search the VIAS Library  |  Index

Limit Rules

Our rules for standard parts in Chapter 1 lead at once to rules for limits. We list these rules in Table 3.3.1. The limit rules can be applied whenever the two limits limx→c f(x) and limx→c g(x) exist.

Table 3.3.1

Standard Part Rule

Limit Rule

st(kb) = k st(b), k real

limx→c kf(x) = k lim/(x)

st(a + b) = st(a) + st(b)

limx→c(f(x) + g(x)) = limx→c f(x) + limx→c g(x)

st(ab) = st(a) · st(b)

limx→c (f(x)g(x)) = limx→c f(x) · limx→c g(x)

st(a/b) = st(a)/st(b), if b≠0

limx→c (f(x)/g(x)) = limx→c f(x)/limx→c g(x), if limx→c g(x) ≠ 0

03_continuous_functions-53.gif ,if a>0

03_continuous_functions-54.gif, if limx→c f(x) > 0

 

 
Home Continuous Functions Limits Limit Rules

Last Update: 2006-11-06