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The limit of the given expression as \( x \to \infty \) is:

\[
\lim_{x \to \infty} \left( \sqrt{4x^2 + 2x} - \sqrt{4x^2 - 2x} \right) = 1
\]

Would you like further details or explanations on the steps involved?

Here are some related questions:
1. How do you simplify square root expressions involving large \(x\)?
2. What happens if the coefficients in the square roots are different?
3. How would the limit change if there was an additional constant term outside the square root?
4. What is the general method for handling limits at infinity with square roots?
5. Could L'Hopital's rule be applied to similar limits?

**Tip:** For limits involving square roots, factoring out the highest power of \(x\) helps simplify expressions.

Find the limit of lim_{x \to \infty} \left( \sqrt{4x^2 + 2x} - \sqrt{4x^2 - 2x} \right)

Learn how to solve the limit problem involving square roots as x approaches infinity. This step-by-step solution simplifies the expression and finds the limit for lim_{x -> infinity} (sqrt(4x^2 + 2x) - sqrt(4x^2 - 2x)) = 1. Suitable for college calculus students or advanced high school students.

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