Tutors on net
Tutors on NetTutors on Net

Definition Of Limits

Limits Assignment / Homework Help
Now that we have looked at how limits arise when we calculate the area of a curved figure let us investigate the numerical and graphical methods of computing limits.

Consider the function f (x) = x 2 + x + 1

We will take a look at how f (x) behaves for values of near 2. The following table will give the values of f (x) for near 2 but not equal to 2.

Online Calculating Limits




x f (x)
1 3
1.5 4.75
1.7 5.59
1.9 6.51
1.99 6.9501
1.999 6.995001






x f (x)
3 13
2.5 9.75
2.2 8.04
2.1 7.51
2.01 7.0501
2.001 7.005001
From the graph and the table we can see that as approaches 2 from the left, f (x) gets closer to 7. Similarly as approaches 2 from the right f (x) approaches 7. We can further verify that f (x) can be made as close to 7 as required by taking sufficiently closer to 2.

In general we can say that
  lim   x2+ x + 1 = 7
x->2

Definition:  Symbolically, we write lim f (x) = L and read this as
                                                       x->a

"The limit of f (x) as x approaches a is L"

If f (x) can be made arbitrarily close to L by taking x sufficiently close to a and xa.

We can also write this as f (x) -> L as x -> a.

Online 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 Limits help are highly qualified. Our tutors have many years of industry experience and have had years of experience providing Limits Homework Help. Please do send us the Limits problems on which you need Help and we will forward then to our tutors for review.


Online Tutor Limits:

We have the best tutors in math in the industry. Our tutors can break down a complex 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 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 Limits tutoring and experience the quality yourself.