Evaluate the Limit

Problem

(lim_x→1)((x−2)/(x2+x−6))

Solution

1. Identify the type of limit by substituting the value x=1 into the expression.

2. Substitute x=1 into the numerator.

1−2=−1

3. Substitute x=1 into the denominator.

1+1−6=−4

4. Evaluate the resulting fraction since it is not an indeterminate form.

(−1)/(−4)=1/4

Final Answer

(lim_x→1)((x−2)/(x2+x−6))=1/4

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