limit calculation

The polynomial sequences always diverge to ±∞, 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:

The rational sequences always have an undetermined form of limit, which we have to solve by dividing by n to highest power:

NOTE: as you can see:

If we have irrational sequences, we only have to do the root of the limit. They always diverge if they exist:

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

If the limit has powers, remember the property:

Examples:

Exercise: calculate:

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