### 2.4 Limits

**Expressing Limits**

The function

**F**has the limit

**L**as

**x**approaches

**a**, written

if the value f(x) can be made as close to the # L as we please by taking x sufficiently close to (but not equal to) a. This means that the limit is the number you are approaching as x gets closer to a.

(The Limit as X approaches a of F(x) is L)

If the equation had a hole where L is the limit would still be the same.

.

(Infinite Limit is true by both sides, increasing without bounds.)

DNE = Does not exist

Your fingers do not meet when tracing.**BUT** if you are looking for or it is possible.

Positive and negative signs indicate direction. Positive = traveling from right to left and Negative = traveling from left to right.

In this case the limits would be:

Evaluating Limits

Direct Substitution

To find the limit without looking at a graph. I plugged in 2 for the equation. 2 squared plus 6 equals 10. 10 is the limit as x approaches 2.

If you have a hole in your graph than you want to try and see the removable discontinuity.

transforms to transforms to

now you can plug in 2 for the equation 4(x+2).

The limit is 16. The limit of 4(x+2) as x approaches 2 is 16.

Limits at Infinity

Rules:

1. If the degree of P(x) is greater than the degree of Q(x) , then the limit will be + or - infinity.

2. If the degree of P(x) is less than the degree of Q(x), then the limit will be a horizontal asympotote at 0.

3. If the degree's of the function are a tie than there will be a horizontal asymptote at the ratio of the leading coefficients.

Example Problem

What is the limit of the function as x approaches infinity?

The function has the same degrees on both top and bottum. You can use the infinity rule that the degree's of the function are a tie. Because they are a tie, this means that the limit is a horizontal asymptote at the ratio of the leading coefficients. In this case the ratio is 17/7.

ANSWER: 17/7

some extra sites on limits:

http://www.coolmath.com/limit1.htm

http://www.calculus-help.com/funstuff/phobe.html

http://curvebank.calstatela.edu/limit/limit.htm

Reminder:

hey nicole....you are up next!

Since it is almost halloween here is a cute joke:

Q: What do you get if you divide the cirucmference of a jack-o-lantern by its diameter?

A: Pumpkin Pi!

## 1 Comments:

I like your first link. I was absent on the day of the lesson, so I was very lost on the concept of limits. The geometric example was an odd but effective way to explain the basic definition of a limit. That website explains calculus concepts in a simple way which is also different from the way it is presented to us. It was very helpful!

Post a Comment

<< Home