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A comment on What's the difference between 0/0 and 1/0?.
This is false. This relies on an assumption not stated - that f is continuous.
For a simple counterexample:
f(x) = 1, x=0
f(x) = x, x!=0
g(x) = x
Limit of the ratio as x approaches 0 is 1.
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This is false. This relies on an assumption not stated - that f is continuous.
For a simple counterexample:
f(x) = 1, x=0
f(x) = x, x!=0
g(x) = x
Limit of the ratio as x approaches 0 is 1.