Evaluate the Limit

Problem

(lim_x→5)((x2−25)/(x−5))

Solution

1. Identify the indeterminate form by substituting x=5 into the expression, which results in 0/0

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

x2−25=(x−5)*(x+5)

3. Simplify the expression by canceling the common factor (x−5) from the numerator and the denominator, noting that x≠5 when taking the limit.

((x−5)*(x+5))/(x−5)=x+5

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

5+5=10

Final Answer

(lim_x→5)((x2−25)/(x−5))=10

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