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## Main Question or Discussion Point

In Dirac's text regarding displacement operator it is given that :-

lim(δx→0)[D*exp(iy)-1]/δx =lim(δx→0) [D-1+iy]/δx = dx + iax

Where dx = displacement operator =lim(δx→0) [D-1]/δx

ax = lim(δx→0) y/ δx

and it is assumed that y tends to zero as δx tends to zero

can anyone explain how the equality of [D*exp(iy)-1] = [D-1+iy] holds good ??

lim(δx→0)[D*exp(iy)-1]/δx =lim(δx→0) [D-1+iy]/δx = dx + iax

Where dx = displacement operator =lim(δx→0) [D-1]/δx

ax = lim(δx→0) y/ δx

and it is assumed that y tends to zero as δx tends to zero

can anyone explain how the equality of [D*exp(iy)-1] = [D-1+iy] holds good ??