5.16 misc

• $\overset{\mathrm{def.}}{=}$ はどうやって出しますか? 昔は \stackrel{}{}, 今だと \overset{}{} を使えだとか。

  \[
    f(x)\stackrel{\mathrm{def.}}{=}x^2+2x+3,\quad
    g(x)\overset{\mathrm{def.}}{=}3x^2+2x+1,\quad
    h(x)\underset{\mathrm{def.}}{=}\sin x.
  \]
  

  $$f(x)\stackrel{\mathrm{def.}}{=}x^2+2x+3,\quad g(x)\overset{\mathrm{def.}}{=}3x^2+2x+1,\quad h(x)\underset{\mathrm{def.}}{=}\sin x.$$

• $\dsp\lim_{y=kx\atop(x,y)\to (0,0)}$ は 上\atop 下 や \genfrac{}{}{0pt}{1}{上}{下}

  \[
    \lim_{y=kx\atop (x,y)\to(0,0)}\frac{x y}{x^2+y^2}
    =
    \lim_{\genfrac{}{}{0pt}{1}{y=kx}{(x,y)\to(0,0)}}\frac{x y}{x^2+y^2}
  \]
  

  $$\lim_{y=kx\atop (x,y)\to(0,0)}\frac{x y}{x^2+y^2} = \lim_{\genfrac{}{}{0pt}{1}{y=kx}{(x,y)\to(0,0)}}\frac{x y}{x^2+y^2}$$