Ges

1. Limits from Tables and Graphs

2. 1. Find lim
𝑥→4
𝑥+2

3. x 2 2.5 3 3.1 3.3 3.5 3.7 3.9 3.99 3.999
f(x)
x 6 5.5 5 4.9 4.7 4.5 4.3 4.1 4.01 4.001
f(x)
Table 1
Table 2
(4,6)
(2,4)
(3,5)
lim
𝑥 → 4
𝑥 +2
6
4 4.5 5 5.1 5.9
5.3 5.5 5.7 5.99
8
5.999
7
7.5 6.7
6.9 6.5 6.3 6.1 6.01 6.001

4. As the value of x gets closer to 4 from
the left or as x approaches 4 from the
left, the value of f(x) approaches 6. As
the value of x gets closer to 4 from
right or as x approaches 4 from the
right, f(x) approaches 6. In other
words, the value of f(x) gets closer and
closer to 6 as the value of x gets closer
and closer to 4 from the either side.
This can be written as follows:
= 6

5. 2. Find lim
𝑥→1
𝑥−3
a. table
b. graph
c. answer
x -2 0 0.1 0.3 0.5 0.7 0.9 0.99 0.999 0.9999
f(x)
x 3 2 1.9 1.7 1.5 1.3 1.1 1.01 1.001 1.0001
f(x)

6. 2. Findlim
𝑥→1
𝑥−3
x -2 0 0.1 0.3 0.5 0.7 0.9 0.99 0.999 0.9999
f(x) -5 -3 -2.9 -2.7 -2.5 -2.3 -2.1 -2.01 -2.001 -2.0001
x 3 2 1.9 1.7 1.5 1.3 1.1 1.01 1.001 1.0001
f(x) 0 -1 -1.1 -1.3 -1.5 -1.7 -1.9 -1.99 -1.999 -1.9999
a. table
b. graph
c. answer
(1,-2)
= -2