Evaluate the Limit

Problem

(lim_x→5)((x2−3*x−10)/(x−5))

Solution

1. Identify the indeterminate form by substituting x=5 into the expression, which results in 0/0

2. Factor the quadratic expression in the numerator by finding two numbers that multiply to −10 and add to −3

3. Rewrite the numerator using the factors (x−5) and (x+2)

4. Cancel the common factor (x−5) from the numerator and the denominator, noting that x≠5

5. Evaluate the limit by substituting x=5 into the remaining simplified expression.

Final Answer

(lim_x→5)((x2−3*x−10)/(x−5))=7

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