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:

Calculating the Limit at a Point

Calculating the Limit at a Point

Calculating the Limit at a Point

Calculating the Limit at a Point

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

However, if Limit at a Point is calculated and 3 is not in the domain, D= R − {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.

Limit of a Piecewise Function.

At x = −1, the side limits are:

Left side limit:Side Limit

Right side limit:Side Limit

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

At x = 1, the side limits are:

Left side limit:Side Limit

Right side limit: Side Limit

There is no limit at x = 1.


Calculation of Limits as x tiende

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

Polynomial Limits

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

Polynomial Limit

Polynomial Limit


If P(x) is a polynomial, then:

Polynomial Limit

Polynomial Limit


Calculation of Limits as x tiende -∞

Limit

Limit

Limit

Limit

Limit

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