Evaluate the Limit

Problem

(lim_x→8)(√(,x))

Solution

1. Identify the type of function. The function ƒ(x)=√(,x) is a radical function that is continuous for all x≥0

2. Apply the direct substitution property for limits. Since x=8 is within the domain of the function, the limit can be found by evaluating the function at that point.

3. Substitute the value x=8 into the expression.

(lim_x→8)(√(,x))=√(,8)

4. Simplify the radical by factoring out the largest perfect square.

√(,8)=√(,4⋅2)

√(,4⋅2)=2√(,2)

Final Answer

(lim_x→8)(√(,x))=2√(,2)

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