Evaluate the Limit

Problem

(lim_x→8)((x2−64)/(x−8))

Solution

1. Identify the indeterminate form by substituting x=8 into the expression, which results in (8−64)/(8−8)=0/0

2. Factor the numerator using the difference of squares formula, a2−b2=(a−b)*(a+b) where a=x and b=8

x2−64=(x−8)*(x+8)

3. Simplify the expression by canceling the common factor (x−8) from the numerator and the denominator, noting that x≠8 as it approaches the limit.

((x−8)*(x+8))/(x−8)=x+8

4. 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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