Evaluate the Limit

Problem

(lim_x→−8)((x2−64)/(x+8))

Solution

1. Identify the form of the limit by substituting x=−8 into the expression.

2. Observe that the substitution results in ((−8)2−64)/(−8+8)=0/0 which is an indeterminate form.

3. Factor the numerator using the difference of squares formula, a2−b2=(a−b)*(a+b)

x2−64=(x−8)*(x+8)

4. Simplify the expression by canceling the common factor (x+8) from the numerator and the denominator.

((x−8)*(x+8))/(x+8)=x−8

5. Evaluate the limit by substituting x=−8 into the simplified expression.

−8−8=−16

Final Answer

(lim_x→−8)((x2−64)/(x+8))=−16

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