How to find the approximate limit of a function using a calculator and/or using excel?

Question

I do not have a specific problem but I need the procedure on how to do it. Thanks

Answer 1

I would use Excel.  For example:

lim(x --> 2) f(x)

I might start with 2 - 1, 2 - .1, 2 - .01, 2 - .001, 2 - .0001 etc and evaluate each of the function values at those points.

However, just to be sure you also have to check this sequence, but only in certain circumstances:

2 + 1, 2 + .1, 2 + .01, 2 + .001, 2 + .0001 etc.

I'll start up Excel and give you an example:

     10^(-previous column) 2 + previous      e raised to the power

..............................     column............of the previous column

1 0.1.................... 2.1........|    8.166169913

2 0.01...................2.01.......|  7.463317347

3 0.001.................2.001......|  7.396448851

4 0.0001...............2.0001.....|  7.389795041

5 0.00001.............2.00001....|  7.38912999

6 0.000001............2.000001..|.7.3...

7 0.0000001......... 2.0000001.|7.389056838

In this case you don't have to use the second sequence.

I hope that gives you the general idea.  The "column" with the 8.... and the 7....s are the e to the power column.

Thanks to the reproduction problems with Yahoo Answers I am having a terrible time trying to line up these columns.