Evaluate the Limit limit as x approaches 3 of (x^2-9)/(x-3)

Problem

(lim_x→3)((x2−9)/(x−3))

Solution

1. Identify the form of the limit by substituting x=3 into the expression, which results in the indeterminate form 0/0

2. Factor the numerator using the difference of squares formula, where x2−9 becomes (x−3)*(x+3)

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

4. Evaluate the limit by substituting x=3 into the remaining simplified expression x+3

Final Answer

(lim_x→3)((x2−9)/(x−3))=6

Want more problems? Check here!