In details

Limits involving infinity


As we know, the expression:

x (x tends to infinity)

it means that x assumes values ​​greater than any real number and x (x tends to less infinity) likewise indicates that x assumes values ​​smaller than any real number.

Example:

The) , that is, as x increase, y tends to zero and the limit is zero.

B) , that is, as x decreases, y tends to zero and the limit is zero.

ç) , ie when x approaches zero by the right of zero or by values ​​greater than zero, y tends to infinity and the limit is infinity.

d) , ie when x tends to zero on the left or by values ​​less than zero, y tends to less infinity

Limit of a polynomial function to

Let the polynomial function . So:

Demonstration:

But:

Soon:

Similarly, for we have:

Examples:

Next: Trigonometric Limits