Evaluate the Limit limit as x approaches 2 of (x^2-4)/(x-2)

Problem

(lim_x→2)((x2−4)/(x−2))

Solution

1. Identify the indeterminate form by substituting x=2 into the expression, which results in (2−4)/(2−2)=0/0

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

x2−4=(x−2)*(x+2)

3. Simplify the expression by canceling the common factor (x−2) from the numerator and the denominator, noting that x≠2 as x approaches 2.

((x−2)*(x+2))/(x−2)=x+2

4. Evaluate the limit by substituting x=2 into the simplified expression.

2+2=4

Final Answer

(lim_x→2)((x2−4)/(x−2))=4

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