MATH 1225 Lecture 8: Sec 2.3 (1)
28 May 2018
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Professor
Sec. 2.3 Calculating Limits Using the Limit Laws
• Limit Laws: Suppose that
c
is constant and the limits
xf
ax
lim
and
xg
ax
lim
exist. Then
o Sum:
xgxfxgxf axaxax limlimlim
o Difference:
xgxfxgxf axaxax limlimlim
o Constant Multiple:
xfcxfc axax limlim
o Product:
xgxfxgxf axaxax • limlimlim
o Quotient:
xg
xf
xg
xf
ax
ax
ax
lim
lim
lim
if
0lim
xg
ax
o Power:
n
ax
n
ax xfxf
limlim
, where
n
is a positive integer
o Root:
n
ax
n
ax xfxf limlim
, where
n
is a positive integer. If
n
is even, assume that
0lim
xf
ax
• Two special limit laws:
o
cc
ax
lim
o
ax
ax
lim
EX: Given that
,3lim,5lim 22 xgxf xx
and
4lim
2
xh
x
, find
2
23
lim xhxf
xg
x
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Document Summary
2. 3 calculating limits using the limit laws: limit laws: suppose that c is constant and the limits. Xg lim lim x a x a xg xf lim x a. Lim xfc lim c x a xgxf xf xg xf: constant multiple, difference, product: Xf xf lim x a lim x a lim x a lim x a: quotient: lim x a xf xg lim x a lim x a x a lim x a. 0 xg if lim x a lim x a xf. Xg: power: lim x a, root: n lim x a xf xf n lim x a. 0 xf lim x a xg xh. 2 xf: two special limit laws: c c lim x a x a lim x a. Ex: for a function f and g whose graph is shown, state the value of each quantity, if it exists. xf.
