Evaluate the Limit

Problem

(lim_x→−10)((x2−100)/(x+10))

Solution

1. Identify the type of limit by substituting x=−10 into the expression.

((−10)2−100)/(−10+10)=0/0

Since this results in an indeterminate form, the expression must be simplified.

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

x2−100=(x−10)*(x+10)

3. Simplify the expression by canceling the common factor (x+10) from the numerator and the denominator.

((x−10)*(x+10))/(x+10)=x−10

4. Evaluate the limit by substituting x=−10 into the simplified expression.

−10−10=−20

Final Answer

(lim_x→−10)((x2−100)/(x+10))=−20

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