# How do you find the limit of #sqrt(9x^2 +x)-(3x)# as x approaches infinity?

by Binomial Expansion

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To find the limit of sqrt(9x^2 + x) - (3x) as x approaches infinity, we can simplify the expression by factoring out x from the square root term. This gives us sqrt(x^2 * (9 + 1/x)) - (3x). Simplifying further, we have x * sqrt(9 + 1/x) - 3x.

Next, we can divide the entire expression by x to get sqrt(9 + 1/x) - 3.

As x approaches infinity, 1/x approaches 0. Therefore, the expression becomes sqrt(9 + 0) - 3, which simplifies to sqrt(9) - 3.

The square root of 9 is 3, so the final limit is 3 - 3, which equals 0.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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