AP Calculus AB/BC 1.5 Limits

AP Calculus: AB/BC Limits Drill 1, Problem 5. Evaluate the limit.

AP CalculusLimits
LanguageEnglish Language
MPAC 1Reasoning with definitions and theorems
MPAC 3Implementing algebraic/computational processes

Transcript

00:25

On the top of the fraction, 11 plus 11 works out as 22...

00:29

...but when we plug it in to the denominator, we get that 11 squared is 121

00:34

and 121 minus 121 is 0.

00:39

Dividing by zero is a big no-no. You can't do that!

00:43

So to avoid that situation, let's try simplifying the bottom.

00:46

x squared minus 121 looks like a difference of two squares...

00:50

...a squared minus b squared equals a plus b times a minus b.

00:56

The square root of 121 is 11. So applying the formula, the bottom simplifies to x plus

01:01

11 times x minus 11.

01:03

The x plus 11 on the top and bottom of the fraction cancel out... and we're left with the

01:08

limit as x approaches 11 from the negative side of 1 over x minus 11.

01:14

Back to the question...it asks us to take the limit as x approaches 11 from the negative side.

01:20

Whenever we deal with limits, it means we get really close to a number from the negative

01:24

side but never actually kiss it.

01:26

If we try plugging in 11 as x again...11 minus 11 still gives us 0 in the denominator...

01:33

...so we can immediately eliminate (A), (B), and (C) because this function is not defined.

01:37

So we're left with D) or (E). We can now start plugging in values smaller

01:42

than 11 that get closer and closer to 11...since we're approaching 11 from the negative side.

01:47

If x equals 10, we get 1 over 10 minus 11, or negative 1.

01:52

If x equals 10.5... then 1 over negative .5 gives us

01:57

an even larger negative number...or negative 2.

02:00

Looks like we're getting more and more negative....and will keep approaching negative infinity...

02:06

So our answer is (E). Done!