Question

e In Example 1,it does not matter that we are trying to find the limit as x approaches 1 for a functic that is not defined at x 1. Why doesn't this matter? Explain. hot oe ese to a but not adol to a In the left column for Example 1, function values for fx) were found for x-values as they approach x 1. Suppose we choose instead to create functions values for the same fix) but we approach x 2 Using your calculator, fill in the following tables. Give your answers to 6 decimal places. f(x) 1.5 1.9 1.99 1.999 1.9999 2.5 2.1 2.01 2.001 2.0001 What value do both of your tables approach as x approaches 2? Find f(2). How do the results from your tables compare to f(2)? Suppose you wanted to find x). Fill in the tables below with appropriate x-values and f x--2 values. Find five x-values for each table. Be careful: x =-2 is a negative number! ㄑㄧ

Answer 1

SOLUTION:

1. Even though the function is not defined at x=1, it is not a problem as the limit to 1 only considers values close to 1 but not exactly 1.

2. 1. f(x) for x<2

      x	f(x)
      1.5	0.400000
      1.9	0.344828
      1.99	0.334448
      1.999	0.333444
      1.9999	0.333344

   2. f(x) for x>2

      x	f(x)
      2.5	0.285714
      2.1	0.322581
      2.01	0.332226
      2.001	0.333222
      2.0001	0.333322

   3. f(x)<2 approaches 0.333344 and f(x)>2 approaches 0.333322 as x approaches 2.

   4. f(2) =  0.333333.

   5. The values in the table gradually approach this value.

3. As x approaches -2:

   1. f(x) for x<-2

      x	f(x)
      -2.5	-0.666667
      -2.1	-0.909091
      -2.001	-0.999001
      -2.0001	-0.999900
      -2.00001	-0.999990

   2. f(x) for x>-2

      x	f(x)
      -1.5	-2.000000
      -1.9	-1.111111
      -1.999	-1.001001
      -1.9999	-1.000100
      -1.99999	-1.000010

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