Infinitesimals equivalents

[LCSphysicist]

Homework Statement:

Is equivalent the infinitesimal segment and the semicircle with diameter equal to this infinitesimal segment?

Relevant Equations:

l/(lpi/2)

dl = Infinitesimal length of the segment.
dlπ/2 = the semicircle length

lim dl-> zero
dl/(dlπ/2) = 2/π, no zero, so the answer would be yes.

But second the book, the answer is no, where am i wrong?

 

[LCSphysicist]

I see, actually I mistook same order and equivalence...

 

[Delta2]

Not sure what you mean by equivalent but they are not equal, they are two different infinitesimals, one is $dx=dl$ and the other is $dy= \frac{\pi}{2}dx=\frac{\pi}{2}dl$.

They are of the same order as you say, they are both linearly dependent on dl so you might say that in this sense they are equivalent.