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# Calculating Limits - PowerPoint PPT Presentation

Calculating Limits. AP Calc 2.2. Computing Limits. As we saw in the last section, graphs can be deceiving! Think of holes shown (or not shown) on the calculator. There is also the possibility that the graph is not readily available.

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## PowerPoint Slideshow about ' Calculating Limits' - sabina

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### Calculating Limits

AP Calc 2.2

• As we saw in the last section, graphs can be deceiving!

• Think of holes shown (or not shown) on the calculator.

• There is also the possibility that the graph is not readily available.

• So we need to know how to calculate limits without pictures!

• Let’s come up with a couple of limits on our own…

• Let’s draw a graph of a constant:

k

• Pick an x – value to approach.

• What is the limit there?

• So:

• Now let’s graph y = x.

y=x

• Pick an x value to approach.

• What is the limit there?

• So:

• Let’s look at the box first…

• BIG FACT:

• A constant factor can be mover through the limit symbol!

• Ex:

• We will be using the 4 step system to find limits:

• Try substituting the given x value first.

• Simplify/Factor Completely

• Try substitution again.

• Sometimes limits DNE!

• Let’s do some examples…

• Ex #1:

• Ex #2:

• Ex #3:

• Ok, Ok… let’s get to some good ones!

• Ex #4:

• Ex #5:

• Ex #6:

• Ex #7:

• If there is no graph available, plug in values approaching the given x – value.

• Ex:

• Let’s make a table of values:

• If there is no graph available, plug in values approaching the given x – value.

• Ex:

• Let’s make a table of values:

So the limit as x approaches

from the left is ∞

• Let’s look at this one:

• Can we just plug in 1?

• How do you simplify this?

• Rationalize! (aka use the conjugate)

• One tip before we do this.

• Don’t do the multiplication of the “unrelated” parts.

• This will make sense in a minute.

• Let’s look at

• Find the following limits:

• Pg. 121 # 1 – 31 odd, #2, and #37