if-lim-x-0-f-x-lim-x-0-g-x-0-when-do-not-use-f-x-to-replace-g-x-

Question Number 211567 by liuxinnan last updated on 13/Sep/24

i f \lim_{x \to 0} f (x) = \lim_{x \to 0} g (x) = 0

w h e n d o n o t u s e f (x) t o r e p l a c e g (x)

Commented by MrGaster last updated on 13/Sep/24

1 . when \lim_{x \to 0} f (x) = \lim_{x \to 0} g (x) = 0

cases where you cannot replace f (x) with g (x) include but are not limitedo

t :

1 . f (x) and g (x) are not equivalent .

infinitesimals

2 . The specific form of thes

function is unknown or complex .

3 . The replacement would affecte

th results of nonlinearo

combinatins .

4 . to indeterminate forms inl

multipication and divisiont

operaions (such as 0 / 0) .

Commented by liuxinnan last updated on 13/Sep/24

t h a n k s