Evaluate the Limit

Problem

(lim_x→25)((√(,x)−5)/(x−25))

Solution

1. Identify the indeterminate form by substituting x=25 into the expression, which results in 0/0

2. Factor the denominator using the difference of squares formula, noting that x−25=(√(,x)−5)*(√(,x)+5)

3. Simplify the expression by canceling the common factor (√(,x)−5) from the numerator and the denominator.

4. Evaluate the limit by substituting x=25 into the remaining simplified expression.

Final Answer

(lim_x→25)((√(,x)−5)/(x−25))=1/10

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