X tends to 0) Lim [(x + 4) ^ 1 / 2-2] / sin3x

(x + 4) ^ 1 / 2 - 2 = x / [(x + 4) ^ 1 / 2 + 2] so the original limit = LIM (x tends to 0) x / sin3x * 1 / [(x + 4) ^ 1 / 2 + 2] obviously when x tends to 0, sin3x is equivalent to 3x, so the original limit = LIM (x tends to 0) x / 3x * 1 / [(x + 4) ^ 1 / 2 + 2] = 1 / 3 * 1 / 4 = 1 / 12, so the limit value is 1 / 12

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