Reference no: EM131100243
Make the given changes in the indicated examples of this section. Then solve the resulting problems. In Example 8, change the numerator to 3x2 - 5x - 2 and find the resulting limit. Disregard references to Examples 6 and 7.
EXAMPLE 6 Behavior of function as x approaches 2
Consider the behavior of 
Because we are not to use x = 2, we use a calculator to set up tables in order to determine values of f(x) as x gets close to 2:
EXAMPLE 7 Limit of function as x approaches 2
Find 
We note immediately that the function is not continuous at x = 2 for division by zero is indicated. Thus, we cannot evaluate the limit by substituting x = 2 into the function. Using a calculator to set up tables (see the margin note), we determine the value that f(x) approaches, as x approaches 2:
We see that the values obtained are identical to those in Example 6. Since 
as x → 2 we have
Therefore, we see that
the limit exists as x→2
the function is not defined at x =2
although
EXAMPLE 8 Limits equal-functions differ
The function 
in Example 7 is the same as the function 2x + 1 in Example 6, except when x = 2 By factoring the numerator of the function of Example 7, and then cancelling, we have
The cancellation in this expression is valid as long as x does not equal 2 for we have division by zero at x = 2 Also, in finding the limit as x → 2 we do not use the value x = 2 therefore
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