Evaluate the Limit

Problem

(lim_x→2)((x^2+3*x−10)/(x^2−4))

Solution

1. Identify the indeterminate form by substituting x=2 into the expression, which results in (2^2+3*(2)−10)/(2^2−4)=0/0

2. Factor the numerator x^2+3*x−10 into (x−2)*(x+5)

3. Factor the denominator x^2−4 as a difference of squares into (x−2)*(x+2)

4. Cancel the common factor (x−2) from the numerator and the denominator, provided x≠2

5. Evaluate the limit by substituting x=2 into the simplified expression (x+5)/(x+2)

Final Answer

(lim_x→2)((x^2+3*x−10)/(x^2−4))=7/4

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