Mathematics
Title: Exercises
Topic: Intuitive concept of limit
Signature: Differential Calculus
Name: _________________________________________ Number:_________________ Major:_____________
Objective: The student will be able to analyze and synthetize the contents of a reading in
order to apply them in the solution of specific problems.
Generic Skills:
 Manages the available resources having in mind the restrictions to reach his goals
and considering his talents (1)
 Deals with problems and challenges having in mind the goals that have been set
(1)
 Proposes solutions to problems based on established methods (5).
Disciplinary skills:
 Explain and interprets the obtained results through mathematical procedures and
compares them with established models or real situations
I. Answer the next questions:
1. Explain with yours owns words the concept of limit.
2. Explain when the limit lim f x does exist.
xa

II. Evaluate the function in the values that are given in the table and complete it. Give the value of the
limit that is requested, and justify it.
1.
f x   x  2 x  3
lim f x  
x
.9
.99
.999
1
1.001
1.01
1.1
4.9
4.99
4.999
5
5.001
5.01
5.1
f x  
x
Because:
3.
x
2.
x 1
2
 x  5 si x  5
f x   
 x  3si x  5
lim f x  
x 5
42
o
43
o
44
o
45
o
46
o
47
o
48
o
Because:
4.
x
Because:
senx   cos x 
sen2 x 
lim f x  
x 45o
3.9
3.99
3.999
4
4.001
4.01
4.1
 x  3 si x  4
f x   
5  x si x  4
lim f x  
x 4
Because:
UPAEP | Mtra. Ana R. Faraco Pérez 1
Mathematics
5.
lim f x  
f x   x  5
2x
x
Because:
lim f x  
7.
x 2
x2  x  6
f x  
x2
Because:
lim f x  
9.
x
-.1
-.01
-.001
0
.001
.01
-.1
 2x 
f  x   1  
3 

1
x
x 0
0.9
0.99
0.999
1
1.001
1.01
1.1
f x  
senx 


cos  x 
2

-.1
-.01
-.001
0
.001
.01
.1
lim f x  
x 0
Because:
10.
-3.1
-3.01
-3.001
-3
-2.999
-2.99
-2.9
x 1
Because:
8.
x
Because:
x 1
f x   2
x 1
2
x
-2.1
-2.01
-2.001
-2
-1.999
-1.99
-1.9
lim f x  
6.
x
.9
.99
.999
1
1.001
1.01
1.1
x
x 1
x5
f x  
x3
lim f x  
x 3
Because:
III. Think about, discuss and answer the next questions.
1. The most common limit encountered in everyday life is the speed limit. Describe how this type
of limit is very different from the concept of limit studied in this session.
UPAEP | Mtra. Ana R. Faraco Pérez 2
Mathematics
2. Your friend says, “The limit is a prediction of what f(a) will be”. Compare and contrast this
statement with the limits that are requested in the next graphic.
f x 
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
lim f x  
x3
lim f x  
x3
lim f x  
x2
lim f x  
x2
lim f x  
x 2
lim f x  
x 2 
lim f x  
x 2 
lim f x  
x 2
lim f x  
x  
UPAEP | Mtra. Ana R. Faraco Pérez 3
DIFFERENTIAL CALCULUS
Sumer 2012