Evaluate the Limit

Problem

(lim_x→∞)(√(,x2+9))

Solution

1. Analyze the behavior of the expression as x increases without bound.

2. Identify the dominant term inside the square root, which is x2

3. Observe that as x→∞ the constant 9 becomes negligible compared to x2

4. Evaluate the limit by noting that √(,x2+9) behaves like √(,x2) which is |x| as x grows very large.

5. Conclude that since x is approaching positive infinity, the value of the expression also increases without bound.

Final Answer

(lim_x→∞)(√(,x2+9))=∞

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