Online One Sided Limits Tutor & Homework Help
One Sided Limits Tutoring Online, Tutor Help With One Sided Limits:
One Sided Limits
We have defined limits as the value that a function f (x) approaches as x
approaches a certain value.
Now x can approach a number 'a' on the number line either from the left or from the left. This gives rise to one sided limits.
Let's take a look at each of this independently. We will consider the function f (x) = x2 and its limit as x approaches 0.
Now x can approach a number 'a' on the number line either from the left or from the left. This gives rise to one sided limits.
Let's take a look at each of this independently. We will consider the function f (x) = x2 and its limit as x approaches 0.
Left – Hand Limit
Consider the limit of f (x) = x2 as x approaches 0 from the left i.e. we look at all the values of f (x) for x < 0.
| x | f (x) |
| -1 | 1 |
| -0.5 | 0.25 |
| -0.2 | 0.04 |
| -0.1 | 0.01 |
| -0.01 | 0.0001 |
| -0.001 | 0.000001 |
As we can see from the graph and the table above f (x) approaches 0 as x approaches 0 from the left.
lim f (x) = 0
x -> a-
This is called the left hand limit of f (x) as x approaches 0.
|
Definition: We say L is the left hand limit of f (x)
if we can make it arbitrarily close to L by taking x sufficiently close to
‘a’ and less than ‘a’.
Symbolically, lim f (x) = L x -> a- |
Online One Sided Limits Help:
If you are stuck with a Limits Homework problem and need help, we have excellent
tutors who can provide you with Homework Help. Our tutors who provide One Sided
Limits help are highly qualified. Our tutors have many years of industry experience
and have had years of experience providing One Sided Limits Homework Help. Please
do send us the One Sided Limits problems on which you need Help and we will forward
then to our tutors for review.
Right – Hand Limit
If we require that x > a in the above discussion then we call it as right
hand limit of f (x) and we write
lim f (x) = L
x -> a+
This can be very well be seen in the graph and table below for f (x) = x2
lim f (x) = L
x -> a+
This can be very well be seen in the graph and table below for f (x) = x2
| x | f (x) |
| 1 | 1 |
| 0.5 | 0.25 |
| 0.2 | 0.04 |
| 0.1 | 0.01 |
| 0.01 | 0.0001 |
| 0.001 | 0.000001 |
We summarize these one sided limits as follows:
|
lim f
(x) = L
x -> a- Left Hand Limit |
lim f
(x) = L
x -> a+ Right Hand Limit |
Finally we conclude that
|
lim f (x) = L
iff lim f
(x) = L and
lim f
(x) = L
x -> a x -> a- x -> a+ |
In words, Limit exists if the right hand limit is equal to the left hand limit.
Online One Sided Tutor Limits:
We have the best tutors in math in the industry. Our tutors can break down a complex
One Sided Limits problem into its sub parts and explain to you in detail how each
step is performed. This approach of breaking down a problem has been appreciated
by majority of our students for learning One Sided Limits concepts.
You will get one-to-one personalized attention through our online tutoring which
will make learning fun and easy. Our tutors are highly qualified and hold advanced
degrees. Please do send us a request for One Sided Limits tutoring and experience
the quality yourself.
