When x → 0, which of the following infinitesimals is (SiNx) / x, 2x-1, (1 / x) / ln (1 + x), x ^ 2 + simx?

The first one uses lobidad cosx, cos0 = 1, the second one directly substitutes into - 1. The third one uses lobidad-1 / X-1 / x ^ 2. When x is close to 0, it is infinite. The fourth one directly substitutes into 0, so choose the fourth one

Let f (x) and x ^ 2 be equivalent infinitesimals, ln (1 + SiNx ^ 4) be infinitesimals of higher order than x ^ n f (x), and x ^ n f (x) be infinitesimals of higher order than e ^ (x ^ 2) - 1?

Note that when x tends to zero, ln (1 + x) is equivalent to x, and SiNx is also equivalent to X
Then ln (1 + SiNx ^ 4) is equivalent to SiNx ^ 4 and then to x ^ 4
therefore
X ^ n * f (x) is of lower order than x ^ 4
And f (x) and x ^ 2 are equivalent infinitesimals
So x ^ n is lower order than x ^ 2
Similarly, when x tends to zero,
E ^ (x ^ 2) - 1 is the equivalent infinitesimal of x ^ 2
Then x ^ n * f (x) is higher order than x ^ 2
F (x) and x ^ 2 are equivalent infinitesimals
So x ^ n is higher order than x ^ 0
So x ^ n is lower order than x ^ 2 and higher order than x ^ 0
So positive integer n = 1

(x ^ 4 + 2x ^ 2-3) / (x ^ 2-3x + 2) is it infinitesimal or infinitesimal when x → 1

(x^4+2x^2-3)/(x^2-3x+2) =(x²+3)(x²-1)/(x-2)(x-1)
=(x²+3)(x-1)(x+1)/(x-2)(x-1)
=(x²+3)(x+1)/(x-2)
When x → 1,
lim(x²+3)(x+1)/(x-2)=-8
So his limit is a real number - 8, not infinity or infinitesimal

When x → 0, which of the following infinitesimals is (SiNx) / x, 2x-1, (1 / x) / ln (1 + x), x ^ 2 + simx?