# How do you find the limit of #x / sqrt (4x^2 + 2x +1) # as x approaches infinity?

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Here is the graph

graph{x / sqrt (4x^2 + 2x +1) [-10, 10, -5, 5]}

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To find the limit of x / sqrt(4x^2 + 2x + 1) as x approaches infinity, we can simplify the expression by dividing both the numerator and denominator by x. This gives us 1 / sqrt(4 + 2/x + 1/x^2). As x approaches infinity, both 2/x and 1/x^2 approach zero. Therefore, the expression simplifies to 1 / sqrt(4) = 1/2. Thus, the limit of x / sqrt(4x^2 + 2x + 1) as x approaches infinity is 1/2.

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