latex study

2023-08-14 本文已影响0人 michael_0x

image.png

proof is as below:

since: x*y = c
so: x = c/y, xAfter = c/(y + Δy )
Δ $\sqrt{P}$ = $\sqrt{\frac{y+Δy}{xAfter}}$ - $\sqrt{\frac{y}{x}}$
= $\sqrt{\frac{y+Δy}{xAfter}}$ - $\sqrt{\frac{y}{x}}$
= $\sqrt{\frac{y+Δy}{c/(y+Δy)}}$ - $\sqrt{\frac{y}{c/y}}$
= $\sqrt{\frac{(y+Δy)^2}{c}}$ - $\sqrt{\frac{y^2}{c}}$
= $\frac{(y+Δy)}{\sqrt{c}}$ - $\frac{(y)}{\sqrt{c}}$
= $\frac{(Δy)}{\sqrt{c}}$
= $\frac{Δy}{L}$