Evaluate the Limit

Problem

(lim_x→1)((x2−1)/(x−1))

Solution

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

2. Factor the numerator using the difference of squares formula, where x2−1=(x−1)*(x+1)

3. Simplify the expression by canceling the common factor (x−1) from the numerator and the denominator.

4. Evaluate the limit by substituting x=1 into the remaining expression x+1

Final Answer

(lim_x→1)((x2−1)/(x−1))=2

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