Evaluate the Limit

Problem

(lim_x→1)((x^2+3*x−4)/(x^2−1))

Solution

1. Identify the indeterminate form by substituting x=1 into the expression, which results in (1^2+3*(1)−4)/(1^2−1)=0/0

2. Factor the numerator x^2+3*x−4 into (x−1)*(x+4) and the denominator x^2−1 into (x−1)*(x+1) using the difference of squares.

3. Simplify the expression by canceling the common factor (x−1) from the numerator and the denominator.

4. Evaluate the limit by substituting x=1 into the remaining simplified expression (x+4)/(x+1)

Final Answer

(lim_x→1)((x^2+3*x−4)/(x^2−1))=5/2

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