مثال للفهم [ عدل ] نأخذ كمثال دالة المربع
x
2
{\displaystyle x^{2}}
x
{\displaystyle x}
x
2
{\displaystyle x^{2}}
x
{\displaystyle x}
lim
x
→
+
∞
x
2
=
+
∞
{\displaystyle \lim _{x\to +\infty }{x^{2}}=+\infty }
lim
x
→
−
∞
x
2
=
+
∞
{\displaystyle \lim _{x\to -\infty }{x^{2}}=+\infty }
+
∞
{\displaystyle +\infty }
f
{\displaystyle f}
∀
M
>
0
,
∃
N
>
0
,
∀
x
∈
D
,
x
>
N
,
f
(
x
)
>
M
{\displaystyle \forall M>0,\exists N>0,\forall x\in {\mathcal {D}},x>N,f(x)>M}
f
{\displaystyle f}
∀
M
>
0
,
∃
N
<
0
,
∀
x
∈
D
,
x
<
N
,
f
(
x
)
>
M
{\displaystyle \forall M>0,\exists N<0,\forall x\in {\mathcal {D}},x<N,f(x)>M}
دالة المربع
−
∞
{\displaystyle -\infty }
f
{\displaystyle f}
∀
M
<
0
,
∃
N
>
0
,
∀
x
∈
D
,
x
>
N
,
f
(
x
)
<
M
{\displaystyle \forall M<0,\exists N>0,\forall x\in {\mathcal {D}},x>N,f(x)<M}
f
{\displaystyle f}
∀
M
<
0
,
∃
N
<
0
,
∀
x
∈
D
,
x
<
N
,
f
(
x
)
<
M
{\displaystyle \forall M<0,\exists N<0,\forall x\in {\mathcal {D}},x<N,f(x)<M}
