Evaluate the Limit

Problem

(lim_x→a)((x2−a2)/(x−a))

Solution

1. Identify the indeterminate form by substituting x=a into the expression, which results in (a2−a2)/(a−a)=0/0

2. Factor the numerator using the difference of squares formula, where x2−a2=(x−a)*(x+a)

3. Simplify the expression by canceling the common factor (x−a) from the numerator and the denominator, provided x≠a

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

Final Answer

(lim_x→a)((x2−a2)/(x−a))=2*a

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