# High School Math : Finding Limits as X Approaches Infinity

## Example Questions

Explanation:

### Example Question #1 : Finding Limits As X Approaches Infinity

Calculate .

The limit does not exist.

Explanation:

This can be rewritten as follows:

We can substitute , noting that as ,

, which is the correct choice.

### Example Question #2 : Finding Limits As X Approaches Infinity

The speed of a car traveling on the highway is given by the following function of time:

What can you say about the car's speed after a long time (that is, as  approaches infinity)?

The speed of the car approaches infinity.

The speed of the car approaches zero.

The speed of the car depends on the starting speed.

Nothing can be concluded from the given function.

The speed of the car approaches a constant number.

The speed of the car approaches infinity.

Explanation:

The function given is a polynomial with a term , such that  is greater than 1.

Whenever this is the case, we can say that the whole function diverges (approaches infinity) in the limit as  approaches infinity.

This tells us that the given function is not a very realistic description of a car's speed for large !