# How do you find the limit of #(sqrt(x^2 – 20x+3) – x)# as x approaches infinity?

Change the form of the expression.

Therefore,

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To find the limit of (sqrt(x^2 – 20x+3) – x) as x approaches infinity, we can simplify the expression by multiplying the numerator and denominator by the conjugate of the expression inside the square root, which is (sqrt(x^2 – 20x+3) + x). This will help eliminate the square root.

After simplifying, we get the expression (x^2 – 20x+3 - x^2) / (sqrt(x^2 – 20x+3) + x).

Simplifying further, we have (-20x+3) / (sqrt(x^2 – 20x+3) + x).

As x approaches infinity, the term -20x becomes insignificant compared to x, and the expression simplifies to 3 / (sqrt(x^2) + x).

Since the square root of x^2 is equal to x for positive values of x, the expression further simplifies to 3 / (x + x).

Finally, the limit of (sqrt(x^2 – 20x+3) – x) as x approaches infinity is 3 / (2x).

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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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