Evaluate the Limit

Problem

(lim_x→−1)((2*x+1)/(x2−3*x+4))

Solution

1. Identify the type of limit by checking if the function is defined at the target value x=−1

2. Evaluate the denominator at x=−1 to ensure it is not zero.

(−1)2−3*(−1)+4=1+3+4=8

3. Apply the direct substitution property for rational functions, as the denominator is non-zero.

(2*(−1)+1)/((−1)2−3*(−1)+4)

4. Simplify the numerator and the denominator to find the final value.

(−2+1)/(1+3+4)=(−1)/8

Final Answer

(lim_x→−1)((2*x+1)/(x2−3*x+4))=−1/8

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