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23 views2 pages

Act 2

Uploaded by

1asectec
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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PrepaTec Campus Chihuahua

AP Calculus
Activity 2. Limit evaluation
Name: _________________________________________ Student ID: _______________ Group: _______
General instructions: solve the following exercises individually according to what is requested in each
of them. All exercises must have a written procedure or they will be considered incorrect.
1. Evaluate the following limits
4𝑥 2 −3𝑥+1
a. 𝑙𝑖𝑚
𝑥→∞ 1−3𝑥 2 5−𝑥 2
f. 𝑙𝑖𝑚
𝑥→−2 𝑥+2

𝑥 2 −𝑥+3 (𝑥−1)2 −(𝑥+1)2


b. 𝑙𝑖𝑚+ = g. 𝑙𝑖𝑚
𝑥→−3 𝑥+3 𝑥→∞ 7𝑥−5

2𝑥−7 𝑥 2 −𝑥
c. 𝑙𝑖𝑚 𝑥 2 +𝑥+3 h. lim
𝑥→∞ 𝑥→0 2𝑥

4𝑥+1 3𝑥 3 +7𝑥 2 +3𝑥+7


d. 𝑙𝑖𝑚+ = i. lim [ ]
𝑥→3 𝑥−3 3𝑥+7
𝑥→−7/3

2𝑥 3 15−3𝑥
e. 𝑙𝑖𝑚 j. lim 4𝑥−20
𝑥→−∞ 𝑥 2 +4 𝑥→5
2. Find all of the discontinuities of the following funcions and classify them. Afterwards, calculate the
functions limit as 𝑥 tends to infinity

𝑥 2 +2𝑥−8
a. 𝑓[𝑥] = 𝑥 3 +7𝑥 2+2𝑥−40

lim 𝑓[𝑥] =
𝑥→∞

16𝑥 3 +24𝑥 2 +5𝑥−3


b. 𝑓[𝑥] = 16𝑥 2 +8𝑥−3

lim 𝑓[𝑥] =
𝑥→∞

𝑥 2 +2𝑥−24
c. 𝑓[𝑥] = 𝑥 2 +4𝑥−12

lim 𝑓[𝑥] =
𝑥→∞

𝑥 3 +𝑥 2 −𝑥−1
d. 𝑓[𝑥] = 𝑥 3 −𝑥 2 −𝑥+1

lim 𝑓[𝑥] =
𝑥→∞

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