Evaluate the Limit

Problem

(lim_x→2)((x2−7*x+10)/(x−2))

Solution

1. Identify the form of the limit by substituting x=2 into the expression.

(2−7*(2)+10)/(2−2)=0/0

Since this is an indeterminate form, the expression must be simplified.

2. Factor the quadratic trinomial in the numerator by finding two numbers that multiply to 10 and add to −7

x2−7*x+10=(x−2)*(x−5)

3. Substitute the factored form back into the limit expression.

(lim_x→2)(((x−2)*(x−5))/(x−2))

4. Simplify the fraction by canceling the common factor (x−2) from the numerator and the denominator.

(lim_x→2)(x−5)

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

2−5=−3

Final Answer

(lim_x→2)((x2−7*x+10)/(x−2))=−3

Want more problems? Check here!