Limits calculation


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:


Number e is the limit:

which is used in the undetermined form of limit 1




Exercise: calculate:




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


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