Taylor Rodriguez Blog #1

Hello! Its Taylor Rodriguez.
This is my first blog of the year so I suppose the first blog of the year calls for a summary of the first chapter of the year.
So this summary will be on estimating limits numerically.
First Ill give some helpful hints that you need to remember when estimating limits numerically
• Remember that estimating limits numerically means to set up and complete the table
The first step to setting up the table is to step up the left side of the graph. To set up the left side of the graph you subtract .1 .01 .001 from the number that X is approaching in the problem and set the subtracted answers to each number into three boxes.
The next box will simply have the number x is approaching in it
The final three boxes will have the results of adding .001 .01 .1 to the number x is approaching respectively.
The first step to estimating the limit is complete

• To complete the table you must enter the given equation into your y=
• After you will hit “2nd” and table and enter in the numbers that you solved for in the seven boxes of the first step.

• now you will fill in the bottom seven boxes of the chart with the results from the table

• (( a quick way to know if you’ve done the steps correctly is to make sure that the box under the box with the number x is approaching should have an error on the table.

Finally to estimate the limit you will read each side toward the number x is approaching and decipher what number each side is headed toward as it approaches the given number x is approaching.
• Remember the three boxes on the left side will read toward the right and the right three boxes will read toward the left

You have the possibility to have two different out comes

• If the numbers on each side of the table match then the number they are headed toward is the estimated limit
• If the numbers on each side of the table do not match the limit does not exist.

I will now give an example of each outcome

EX:1
Lim X-> 0
F(x)= x/ squareroot of (x + 1) -1
The top half of the table will read
[-.1] [-.01] [-.001] [0] [.001] [.01] [.1]
The bottom half of the table will read
[1.9487] [1.995] [1.995] [ERROR] [2.0005] [2.005] [2.0488]
From the left the numbers are approaching 2
From the right the numbers are also approaching 2
Therefore the estimated limit is 2

Ex:2
Lim X-> 0
F(x)= sin 1/x
The top half of the table will read
[2/pi] [2/3pi] [2/5pi] [0] [2/7pi] [2/9pi] [2/11pi]
The bottom half of the table will read
[1] [-1] [1] [ERROR] [-1] [1] [-1]
From the left the numbers are not approaching anything
From the right the numbers are also not approaching anything
Therefore the estimated limit DNE