Evaluate the Limit

Problem

(lim_x→5)((√(,x+5)−3)/(x−4))

Solution

1. Identify the type of limit by substituting the value x=5 into the expression.

2. Substitute the value x=5 into the numerator and denominator.

(√(,5+5)−3)/(5−4)

3. Simplify the expression inside the square root.

(√(,10)−3)/1

4. Evaluate the final result since the denominator is not zero and the expression is defined.

√(,10)−3

Final Answer

(lim_x→5)((√(,x+5)−3)/(x−4))=√(,10)−3

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