Originally Posted by

**integral** $\displaystyle

f(x) = \left\{

\begin{array}{lr}

x=3,\, \, if\, \, .5<x<1.325 \\

y=.5,\, \, if\, \, -3<y<-2.5

\end{array}

\right.

$

$\displaystyle

f(x) = \left\{

\begin{array}{lr}

x=-2,\, \, if\, \, .5<x<0.994 \\

\end{array}

\right.

$

$\displaystyle

\underbrace{f(x) = \left\{

\begin{array}{lr}

y=-x, \,\, if \,\, -1<x<-.5\\

y=x+2,\, \, if\, \, -1.5<x<-1\\

y=x+1,\,\, if \,\, -0.5<x<0\\

y=-x+1 \,\, if \,\, 0<x<.5

\end{array}

\right.}

$

As:

$\displaystyle

\Delta \left\{

\begin{array}{lr}

y=x,\, \, if\, \, -1<x<1 \\

y=-x,\, \, if\, \, -1<x<-1

\end{array}

\right. \to 0

$

for: $\displaystyle y=7x^4$