Calculating Limits
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.
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.
