With the use of a graphing utility, if possible, determine the left- and right-hand limits of the following function as
approaches 0. If the function has a limit as
approaches 0, state it. If not, discuss why there is no limit.
We can use a graphing utility to investigate the behavior of the graph close to
Centering around
we choose two viewing windows such that the second one is zoomed in closer to
than the first one. The result would resemble
[link] for
by
Even closer to zero, we are even less able to distinguish any limits.
The closer we get to 0, the greater the swings in the output values are. That is not the behavior of a function with either a left-hand limit or a right-hand limit. And if there is no left-hand limit or right-hand limit, there certainly is no limit to the function
as
approaches 0.
A function has a limit if the output values approach some value
as the input values approach some quantity
See
[link] .
A shorthand notation is used to describe the limit of a function according to the form
which indicates that as
approaches
both from the left of
and the right of
the output value gets close to
A function has a left-hand limit if
approaches
as
approaches
where
A function has a right-hand limit if
approaches
as
approaches
where
A two-sided limit exists if the left-hand limit and the right-hand limit of a function are the same. A function is said to have a limit if it has a two-sided limit.
A graph provides a visual method of determining the limit of a function.
If the function has a limit as
approaches
the branches of the graph will approach the same
coordinate near
from the left and the right. See
[link] .
A table can be used to determine if a function has a limit. The table should show input values that approach
from both directions so that the resulting output values can be evaluated. If the output values approach some number, the function has a limit. See
[link] .
A graphing utility can also be used to find a limit. See
[link] .
Section exercises
Verbal
Explain the difference between a value at
and the limit as
approaches
The value of the function, the output, at
is
When the
is taken, the values of
get infinitely close to
but never equal
As the values of
approach
from the left and right, the limit is the value that the function is approaching.
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
![Graph of a sinusodial function zoomed in at [-2, 2] by [-3, 3].](/ocw/mirror/col11667/m49452/CNX_Precalc_Figure_12_01_011F.jpg)
![Graph of the same sinusodial function as in the previous image zoomed in at [-0.1, 0.1] by [-3. 3].](/ocw/mirror/col11667/m49452/CNX_Precalc_Figure_12_01_012F.jpg)
