Evaluate the Limit

Problem

(lim_x→−6)((x2−36)/(x+6))

Solution

1. Identify the type of limit by substituting x=−6 into the expression, which results in the indeterminate form 0/0

2. Factor the numerator using the difference of squares formula, a2−b2=(a−b)*(a+b) where a=x and b=6

x2−36=(x−6)*(x+6)

3. Simplify the expression by canceling the common factor (x+6) from the numerator and the denominator.

((x−6)*(x+6))/(x+6)=x−6

4. Evaluate the limit by substituting x=−6 into the simplified expression.

−6−6=−12

Final Answer

(lim_x→−6)((x2−36)/(x+6))=−12

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