Evaluate the Limit

Problem

(lim_x→2)((x2+x−6)/(x−2))

Solution

1. Identify the type of limit by substituting x=2 into the expression, which results in the indeterminate form 0/0

2. Factor the quadratic expression in the numerator by finding two numbers that multiply to −6 and add to 1

x2+x−6=(x+3)*(x−2)

3. Simplify the rational expression by canceling the common factor of (x−2) from the numerator and the denominator.

((x+3)*(x−2))/(x−2)=x+3

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

2+3=5

Final Answer

(lim_x→2)((x2+x−6)/(x−2))=5

Want more problems? Check here!