Section 1.5
The Limit of a Function
Definition: We write
And say
lim xa f ( x)  L
“The limit of f(x), as x approaches a, equals L”
If we can make the values of f(x) arbitrarily close to L (as close to L as we like)
by taking x to be sufficiently close to a (on either side of a) but not equal to a.
y  sin x / x
 lim x0 
sin x
1
x
Example 2: Estimate the value of lim t 0
lim t 0
t2  9 3 1

2
6
t
t
t2  9 3
t2
.1
0.16662
.01
0.001
-0.001
-.01
-0.1
0.16667
0.16667
0.16667
0.16667
0.16662
t2  9 3
t2
lim x0 sin

x
 1
 lim x0 sin

x
 Does Not Exist