Evaluate the Limit

Problem

(lim_x→4)((x2−7*x+12)/(x−4))

Solution

1. Identify the indeterminate form by substituting x=4 into the expression, which results in (4−7*(4)+12)/(4−4)=0/0

2. Factor the numerator x2−7*x+12 by finding two numbers that multiply to 12 and add to −7

3. Rewrite the quadratic expression as (x−3)*(x−4)

4. Simplify the fraction by canceling the common factor (x−4) from the numerator and the denominator, noting that x≠4 as we approach the limit.

5. Evaluate the limit by substituting x=4 into the remaining expression x−3

Final Answer

(lim_x→4)((x2−7*x+12)/(x−4))=1

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