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pls solve ! 10 points?
with steps pls! thank you
1 Answer
- 6 years agoFavorite Answer
sqrt(x^2 + 2x) - sqrt(x^2 - 2x) =>
(sqrt(x^2 + 2x) - sqrt(x^2 - 2x)) * (sqrt(x^2 + 2x) + sqrt(x^2 - 2x)) / (sqrt(x^2 + 2x) + sqrt(x^2 - 2x)) =>
(x^2 + 2x - x^2 - (-2x)) / (x * sqrt(1 + 2/x) + x * sqrt(1 - 2/x)) =>
4x / (x * (sqrt(1 + 2/x) + sqrt(1 - 2/x))) =>
4 / (sqrt(1 + 2/x) + sqrt(1 - 2/x))
x goes to infinity
4 / (sqrt(1 + 0) + sqrt(1 - 0)) =>
4 / (sqrt(1) + sqrt(1)) =>
4 / (1 + 1) =>
4/2 =>
2
EDIT:
Same limit even when x goes to negative infinity
