MATH 1225 Lecture Notes - Lecture 9: Asymptote
28 May 2018
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Sec. 2.2 continue The Limit of a Function
• Definition of an infinite limit:
o Let
xf
be a function defined on both sides of
a
, except possibly at
a
itself. Then
xf
ax
lim
means that the values of
xf
can be made arbitrarily large (as large as we please) by taking
x
sufficiently close to
a
, but not equal to
a
.
o Let
xf
be a function defined on both sides of
a
, except possibly at
a
itself. Then
xf
ax
lim
means that the values of
xf
can be made arbitrarily large negative by taking
x
sufficiently close to
a
, but not equal to
a
.
• Does
xf
ax
lim
equal to
exist or does not exist?
• When do we write
and when do we write DNE? Consider the examples below.
EX:
1. What is
xf
x2
lim
and
xf
x4
lim
2. What is
xg
x2
lim
and
xg
x
2
lim
3. What is
xh
x3
lim
? What is
xh
x3
lim
?
4. What is
xf
x2
lim
,
xf
x
2
lim
, and
xf
x
2
lim
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Document Summary
2. 2 continue the limit of a function: definition of an infinite limit, let be a function defined on both sides of a , except possibly at a itself. Xf sufficiently close to a , but not equal to a . can be made arbitrarily large (as large as we please) by taking x xf lim x a xf lim x a. Xf: let be a function defined on both sides of a , except possibly at a itself. Then means that the values of a , but not equal to a . Xf can be made arbitrarily large negative by taking x sufficiently close to: does. Xf: why is there a hole at. 1 x instead of a vertical asymptote? y x. , find the following, if possible: determine the domain of. Xf: definition of vertical asymptote: lim x. The vertical line ax is called a vertical asymptote of the curve y .
