C1-1 Name___________________________________BDFM?_________Why?_____________________________
1. Complete the table and investigate the limit.
𝑥3 + 1
lim
𝑥→−1 𝑥 + 1
𝒙
-1.1
-1.01
-1.001
-1
-0.999
-0.99
-0.9
𝑥3 + 1
𝑓(𝑥) =
𝑥 +1
2. Use the graph to investigate each limit.
a. lim − 𝑓(𝑥)= _______
b.
c. lim 𝑓(𝑥) = _______
d. f(–3) = _______
e. lim f ( x) = _______
f. lim f ( x) = _______
g. lim+ 𝑓(𝑥) = _______
h. lim 𝑓(𝑥)= _______
i. f(5) = _______
j. lim f ( x) = _______
𝑥→−3
𝑥→−3
x →5−
x→0
𝑥→5
lim 𝑓(𝑥)= _______
𝑥→−3+
𝑥→5
x →−2−
C1-1Name___________________________________BDFM?_________Why?_____________________________
1. Complete the table and investigate the limit.
𝑥3 + 1
lim
𝑥→−1 𝑥 + 1
𝒙
-1.1
-1.01
-1.001
-1
-0.999
-0.99
-0.9
𝑥3 + 1
𝑓(𝑥) =
𝑥 +1
2. Use the graph to investigate each limit.
a. lim − 𝑓(𝑥)= _______
b.
c. lim 𝑓(𝑥) = _______
d. f(–3) = _______
e. lim f ( x) = _______
f. lim− f ( x) = _______
g. lim+ 𝑓(𝑥) = _______
h. lim 𝑓(𝑥)= _______
i. f(5) = _______
j. lim − f ( x) = _______
𝑥→−3
𝑥→−3
x→0
𝑥→5
lim 𝑓(𝑥)= _______
𝑥→−3+
x →5
𝑥→5
x →−2
3. Using the correct limit notation, use the sentence to write the limit.
2
“The limit as x approaches 7 of 𝑥+5 is equal to 1/6.
4. Sketch a graph with the properties:
lim 𝑓(𝑥) = 0 ;
lim− 𝑓(𝑥) = −2 ;
𝑥→−1
𝑥→2
lim 𝑓(𝑥) = −2 ;𝑓(−1) is not defined ;
𝑥→2+
𝑓(2) = −2
3. Using the correct limit notation, use the sentence to write the limit.
2
“The limit as x approaches 7 of 𝑥+5 is equal to 1/6.
4. Sketch a graph with the properties:
lim 𝑓(𝑥) = 0 ;
lim− 𝑓(𝑥) = −2 ;
𝑥→−1
𝑥→2
lim 𝑓(𝑥) = −2 ;𝑓(−1) is not defined ;
𝑥→2+
𝑓(2) = −2