1 answer

E In Example 1,it does not matter that we are trying to find the limit as x approaches 1 for

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
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

Answers

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.
    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.

  2. 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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