The order of 1-x and 1 / 2 (1-x ^ 2) infinitesimal when x tends to 1

The order of 1-x and 1 / 2 (1-x ^ 2) infinitesimal when x tends to 1

The comparison derivative: (1-x) = - 1; [(1-x & # 178;) / 2] '= - x = - 1, equal

X → 1, (1-x ^ 3) ^ 2 is the infinitesimal of order (1-x)? What do you think

This problem expands (1-x ^ 3) ^ 2 (1-x) ^ 2 (1 + X + x ^ 2) ^ 2. When x → 1, the limit is (1-x) ^ 2
So LIM (1-x ^ 3) ^ 2 / (1-x) ^ 2 = (1 + X + x ^ 2) ^ 2 = 9
It's infinitesimal of order 2

F = 2 ^ x + 2 ^ X-2, when X - > 0, are f and X equivalent infinitesimals of the same order?

Because Lim [2 ^ x + 3 ^ X-2] / x = Lim [2 ^ x + 3 ^ X-2] '/ X' = Lim [2 ^ x + 3 ^ x] = 1 + 1 = 2
Then 2 ^ x + 3 ^ X-2 is the infinitesimal of the same order of X, not the equivalent infinitesimal