Evaluate the Limit

Problem

(lim_x→−2)((x2−3*x−10)/(x+2))

Solution

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

2. Factor the quadratic expression in the numerator by finding two numbers that multiply to −10 and add to −3

3. Rewrite the numerator as (x−5)*(x+2)

4. Cancel the common factor of x+2 from both the numerator and the denominator, noting that x≠−2

5. Evaluate the limit by substituting x=−2 into the remaining expression x−5

Final Answer

(lim_x→−2)((x2−3*x−10)/(x+2))=−7

Want more problems? Check here!