# 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.