Evaluate the Limit

Problem

(lim_x→−7)((x2−49)/(x+7))

Solution

1. Identify the indeterminate form by substituting x=−7 into the expression, which results in 0/0

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

x2−49=(x−7)*(x+7)

3. Simplify the expression by canceling the common factor (x+7) from the numerator and the denominator.

((x−7)*(x+7))/(x+7)=x−7

4. Evaluate the limit by substituting x=−7 into the simplified expression.

−7−7=−14

Final Answer

(lim_x→−7)((x2−49)/(x+7))=−14

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