Limits of functions

# Limits calculation

Examples:

NOTE: remember that:

In infinite limits with polynomial functions, the limit is always ±∞ depending on the sign of the coefficient of the greatest degree term:

**Undetermined forms of limits**are the limits that are different depending on the situation. They are:

Infinite limits with rational functions always have an undetermined form of limit, which we have to solve by dividing by x to the highest power:

In the end:

If we have irrational functions:

We can find an undetermined form of limit if we subtract square roots, then we have to use the conjugate to solve it:

If a is -∞, then we change:

For example:

When *a* is not infinite, we can find other undetermined forms of limit:

Other examples:

If the limit has powers, remember the property:

Examples:

**Number e** is the limit:

which is used in the undetermined form of limit 1^{∞}

Example:

**Exercise**: calculate:

Solutions: a) 0; b) 1/2; c) 0; d) 1; e) -∞

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