Unit 1: Introduction to Calculus
→
=
limx
afx
L
•
X is a veryvery close to but not equal to ‘a’
o
Must be a number on each side of a
•
The limit of the function only exist if the limit from the left is equal to the limit from
the right
→ 
=
→ + ( )
limx
a fx
limx
a f x
•
One sided limits
•
The limit of f(x) as x approaches to infinity is 0
Properties:
1.
→
=
limx
ak
k
2.
→
=
limx
ax
a
3. Limit of a sum or Difference
→
limx
afx
±
=
→
gx
limx
afx
±
→
( )
limx
ag x
4. Limit of a Constant
→
( )=
→
( )
limx
acf x
c limx
af x
5. Limit of a product
→
( )=
→
×
→
( )
limx
afxg x
limx
afx
limx
ag x
6.
Limit of a quotient
→
( ) ( )=
→
( )
→
( )
limx
af x g x
limx
af x limx
ag x
Note:
→
( )≠
limx
ag x
0
7. Limit of a power
→ [
] =[
→
( )]
limx
a fx n
limx
af x n
Ex)
→
+
 =
→
+
→

→
limx
3x2 2x 6
limx
3x2 limx
32x limx
36
[
→
] +
→

→
limx
3x 2
2limx
3x
limx
36
[3]
2
+ 2[3]6
9
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When x
→
0 divide top & bottom (every term) by highest term
Ex)
( )=
≤

>
f x
x2 if x
14 1 if x 1
(i).
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 Spring '99
 George
 Calculus, lim, Continuous function, Difference limx→afx± gx=limx→afx±, quot ient limx→af

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