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- Calculus volume 1
- Limits
- The limit of a function
Key concepts
- A table of values or graph may be used to estimate a limit.
- If the limit of a function at a point does not exist, it is still possible that the limits from the left and right at that point may exist.
- If the limits of a function from the left and right exist and are equal, then the limit of the function is that common value.
- We may use limits to describe infinite behavior of a function at a point.
Key equations
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Intuitive Definition of the Limit
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Two Important Limits
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One-Sided Limits
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Infinite Limits from the Left
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Infinite Limits from the Right
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Two-Sided Infinite Limits
and
and
For the following exercises, consider the function
[T] Complete the following table for the function. Round your solutions to four decimal places.
x |
|
x |
|
0.9 |
a. |
1.1 |
e. |
0.99 |
b. |
1.01 |
f. |
0.999 |
c. |
1.001 |
g. |
0.9999 |
d. |
1.0001 |
h. |
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What do your results in the preceding exercise indicate about the two-sided limit
Explain your response.
does not exist because
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For the following exercises, consider the function
[T] Make a table showing the values of
f for
and for
Round your solutions to five decimal places.
x |
|
x |
|
−0.01 |
a. |
0.01 |
e. |
−0.001 |
b. |
0.001 |
f. |
−0.0001 |
c. |
0.0001 |
g. |
−0.00001 |
d. |
0.00001 |
h. |
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In the following exercises, use the given values to set up a table to evaluate the limits. Round your solutions to eight decimal places.
[T]
x |
|
x |
|
−0.1 |
a. |
0.1 |
e. |
−0.01 |
b. |
0.01 |
f. |
−0.001 |
c. |
0.001 |
g. |
−0.0001 |
d. |
0.0001 |
h. |
a. 1.98669331; b. 1.99986667; c. 1.99999867; d. 1.99999999; e. 1.98669331; f. 1.99986667; g. 1.99999867; h. 1.99999999;
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[T] In the following exercises, set up a table of values to find the indicated limit. Round to eight digits.
x |
|
x |
|
0.9 |
a. |
1.1 |
e. |
0.99 |
b. |
1.01 |
f. |
0.999 |
c. |
1.001 |
g. |
0.9999 |
d. |
1.0001 |
h. |
a. −0.80000000; b. −0.98000000; c. −0.99800000; d. −0.99980000; e. −1.2000000; f. −1.0200000; g. −1.0020000; h. −1.0002000;
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z |
|
z |
|
−0.1 |
a. |
0.1 |
e. |
−0.01 |
b. |
0.01 |
f. |
−0.001 |
c. |
0.001 |
g. |
−0.0001 |
d. |
0.0001 |
h. |
a. −37.931934; b. −3377.9264; c. −333,777.93; d. −33,337,778; e. −29.032258; f. −3289.0365; g. −332,889.04; h. −33,328,889
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Questions & Answers
the study of living organisms and their interactions with one another and their environments
AI-Robot
HOW CAN MAN ORGAN FUNCTION
the diagram of the digestive system
allimentary cannel
Ogenrwot
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
Genetics is the study of heredity
Misack
how does twins formed?
Misack
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
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Source:
OpenStax, Calculus volume 1. OpenStax CNX. Feb 05, 2016 Download for free at http://cnx.org/content/col11964/1.2
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