LIM (x approaches infinity) f (2x) - f (0) / x = 1 / 2, then f (0) derivative | Math enthusiast | Mathematical art

LIM (x approaches infinity) f (2x) - f (0) / x = 1 / 2, then f (0) derivative

No, it should be x → 0, right?
The main idea is to work out the definition of F '(0), so divide by 2x and deal with the redundant part
lim(x→0)(f(2x)-f(0))/x=lim(x→0)(f(2x)-f(0))/(2x)*2=f'(0)*2=1/2
f'(0)=1/4

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