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.
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ma management ho
Amisha
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
belatari
Amisha
1st year ho
Amisha
nd u
Amisha
ahh
Amisha
kaha biratnagar
Amisha
ys
Amisha
kina k vo
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.