Evaluate the Limit

Problem

(lim_x→8)(√(,4*x2+x)−2*x)

Solution

1. Identify the type of limit by substituting the value x=8 into the expression.

2. Substitute the value 8 for x in the expression √(,4*x2+x)−2*x

3. Calculate the value inside the square root: 4*(8)2+8=4*(64)+8=256+8=264

4. Calculate the second term: 2(8) = 16$.

5. Simplify the resulting expression √(,264)−16

6. Factor the square root by finding the largest perfect square divisor of 264 which is 4

7. Simplify the radical: √(,264)=√(,4⋅66)=2√(,66)

Final Answer

(lim_x→8)(√(,4*x2+x)−2*x)=2√(,66)−16

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