Evaluate the Limit

Problem

(lim_x→∞)(√(,x2+1))

Solution

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

2. Observe that as x→∞ the term x2 also approaches ∞

3. Determine that adding 1 to an infinitely large value does not change its limit, so x2+1→∞

4. Evaluate the square root of an expression approaching infinity, which also approaches infinity.

Final Answer

(lim_x→∞)(√(,x2+1))=∞

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