Comments by "MC116" (@angelmendez-rivera351) on "Limit of sqrt(9x^2 + 3x) - 3x as x approaches infinity" video.

  1. sqrt(9·x^2 + 3·x) – 3·x = sqrt(y^2 + y) – y, where y = 3·x. Letting x —> ∞ is indeed equivalent to letting y —> ∞, so we consider lim sqrt(y^2 + y) – y (y —> ∞) = lim sqrt(y)·(sqrt(y + 1) – sqrt(y)) (y —> ∞) = lim sqrt(y)/(sqrt(y + 1) + sqrt(y)) (y —> ∞) = lim 1/(sqrt(1 + 1/y) + 1) (y —> ∞) = lim 1/(sqrt(1 + y) + 1) (y > 0, y —> 0) = 1/2.
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  2. f(x) ~ g(x) means lim f(x)/g(x) = 1, it does not mean lim f(x) – g(x) = 0, or anything of the sort.
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