Calculating the Limit at a Point

If f(x) is a common function (polynomial, rational, radical, exponential, logarithmic, etc.) and is defined at point a, then:

cannot be calculated because the domain is in the interval [0, ∞), therefore the values that are close to −2 cannot be taken.

However, if is calculated and 3 is not in the domain, D= − {2, 3}, domain values as close to 3 as possible can be taken.

The best Maths tutors available
1st lesson free!
Intasar
4.9
4.9 (26 reviews)
Intasar
£36
/h
1st lesson free!
Matthew
5
5 (17 reviews)
Matthew
£25
/h
1st lesson free!
Paolo
4.9
4.9 (13 reviews)
Paolo
£25
/h
1st lesson free!
Dr. Kritaphat
4.9
4.9 (7 reviews)
Dr. Kritaphat
£49
/h
1st lesson free!
Ayush
5
5 (28 reviews)
Ayush
£60
/h
1st lesson free!
Petar
4.9
4.9 (9 reviews)
Petar
£27
/h
1st lesson free!
Farooq
5
5 (14 reviews)
Farooq
£40
/h
1st lesson free!
Tom
5
5 (9 reviews)
Tom
£22
/h
1st lesson free!
Intasar
4.9
4.9 (26 reviews)
Intasar
£36
/h
1st lesson free!
Matthew
5
5 (17 reviews)
Matthew
£25
/h
1st lesson free!
Paolo
4.9
4.9 (13 reviews)
Paolo
£25
/h
1st lesson free!
Dr. Kritaphat
4.9
4.9 (7 reviews)
Dr. Kritaphat
£49
/h
1st lesson free!
Ayush
5
5 (28 reviews)
Ayush
£60
/h
1st lesson free!
Petar
4.9
4.9 (9 reviews)
Petar
£27
/h
1st lesson free!
Farooq
5
5 (14 reviews)
Farooq
£40
/h
1st lesson free!
Tom
5
5 (9 reviews)
Tom
£22
/h
First Lesson Free>

Calculating the Limit of a Piecewise Function

First, study the side limits.

If they coincide, this is the value of the limit.

If they do not coincide, the limit does not exist.

.

At x = −1, the side limits are:

Left side limit:

Right side limit:

In both cases, they coincide, therefore, the limit is 1.

At x = 1, the side limits are:

Left side limit:

Right side limit:

There is no limit at x = 1.

Calculation of Limits as x ∞

To calculate the limit of a function as x ∞, x is replaced by ∞.

Polynomial Limits

The limit as x ∞ of a polynomial function is +∞ or −∞ whether the term of highest degree is positive or negative.

If P(x) is a polynomial, then:

Calculation of Limits as x -∞

There is no limit, because the radical has negative values.

Need a Maths teacher?

Did you like the article?

1 Star2 Stars3 Stars4 Stars5 Stars 5.00/5 - 1 vote(s)
Loading...

Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.