To determine whether a
piecewise function is continuous or discontinuous, in addition to checking the boundary points, we must also check whether each of the functions that make up the piecewise function is continuous.
Given a piecewise function, determine whether it is continuous.
Determine whether each component function of the piecewise function is continuous. If there are discontinuities, do they occur within the domain where that component function is applied?
For each boundary point
of the piecewise function, determine if each of the three conditions hold.
Determining whether a piecewise function is continuous
Determine whether the function below is continuous. If it is not, state the location and type of each discontinuity.
The two functions composing this piecewise function are
on
and
on
The sine function and all polynomial functions are continuous everywhere. Any discontinuities would be at the boundary point,
At
let us check the three conditions of continuity.
Condition 1:
Because all three conditions are not satisfied at
the function
is discontinuous at
A continuous function can be represented by a graph without holes or breaks.
A function whose graph has holes is a discontinuous function.
A function is continuous at a particular number if three conditions are met:
Condition 1:
exists.
Condition 2:
exists at
Condition 3:
A function has a jump discontinuity if the left- and right-hand limits are different, causing the graph to “jump.”
A function has a removable discontinuity if it can be redefined at its discontinuous point to make it continuous. See
[link] .
Some functions, such as polynomial functions, are continuous everywhere. Other functions, such as logarithmic functions, are continuous on their domain. See
[link] and
[link] .
For a piecewise function to be continuous each piece must be continuous on its part of the domain and the function as a whole must be continuous at the boundaries. See
[link] and
[link] .
Section exercises
Verbal
State in your own words what it means for a function
to be continuous at
Informally, if a function is continuous at
then there is no break in the graph of the function at
and
is defined.
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
