Commonly used equivalent infinitesimal x ^ 4-2x ^ 2 ~ - 2x ^ 2, which I can't understand at all X tends to zero | Math enthusiast | Mathematical art

Commonly used equivalent infinitesimal x ^ 4-2x ^ 2 ~ - 2x ^ 2, which I can't understand at all X tends to zero

When x → 0, x ^ 4 is infinitesimal of higher order than x ^ 2, so it can be considered as 0, so x ^ 4-2x ^ 2 ~ - 2x ^ 2

When x approaches zero, e ^ 2x cos x is infinitesimal of higher order / lower order / equivalent / unequal of the same order compared with sin X

A:
LIM (x → 0) (e ^ 2x cosx) / SiNx
=lim(x→0) (2e^2x+sinx)/cosx
=(2+0)/1
=2
Is infinitesimal of the same order

The limit of 1-cosx / x ^ 2-x ^ 4 is x → 0

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