Evaluate the Limit

Problem

(lim_x→−1)((x2+3*x+2)/(x2+1))

Solution

1. Identify the type of limit by substituting the value x=−1 into the expression to check for indeterminacy.

2. Substitute the value into the numerator: (−1)2+3*(−1)+2=1−3+2=0

3. Substitute the value into the denominator: (−1)2+1=1+1=2

4. Evaluate the resulting fraction since the denominator is not zero.

5. Simplify the fraction 0/2 to find the final limit value.

Final Answer

(lim_x→−1)((x2+3*x+2)/(x2+1))=0

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