Evaluate the Limit

Problem

(lim_x→1)(√(,3*x−2))

Solution

1. Identify the type of function. The function ƒ(x)=√(,3*x−2) is a composition of a square root function and a linear function.

2. Check the domain. The expression inside the square root, 3*x−2 must be non-negative. At x=1 3(1) - 2 = 1$, which is in the domain.

3. Apply the direct substitution property for limits. Since the function is continuous at x=1 the limit is equal to the value of the function at that point.

4. Substitute x=1 into the expression.

√(,3*(1)−2)

5. Simplify the arithmetic inside the radical.

√(,3−2)=√(,1)

6. Evaluate the square root.

√(,1)=1

Final Answer

(lim_x→1)(√(,3*x−2))=1

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