Find the limit LIM (sinxy) / y X - > a Y - > 0

Find the limit LIM (sinxy) / y X - > a Y - > 0

If X - > A, Y - > 0, then XY - > 0
(SiNx and XY are continuous functions)
So we have an important limit: LIM (sinxy) / y = limx [(sinxy) / XY]
=lim*lim（sinxy) / xy
=a*1
=a

Why is the 1 / X power-1 of LIM (x tends to 0 +) 2 + ∞ and the 1 / X power-1 of LIM (x tends to 0 -) 2 - 1?

X tends to zero+
1/x→+∞
Then 2 ^ (1 / x) → + ∞
And X tends to zero-
1/x→-∞
Then 2 ^ (1 / x) → 0
So the left limit is - 1

X tends to 0 sin (x-x ^ 2) of Tan (2x + x ^ 3) to find the limit, please write down the steps

Using Equivalent Infinitesimal Substitution,
sinx~x,tanx~x,
——》Original formula = limx → 0 (2x-x ^ 3) / (x-x ^ 2)
=limx→0 (2-x^2)/(1-x)
=(2-0)/(1-0)
=2.