Upload
others
View
2
Download
0
Embed Size (px)
Citation preview
−= + ⋅ ∈ ∈
•
•
•
•
•
≤ ≤
= =
−= = −
→ ∞ + −
→ ∞ →
→ −∞
−
−
′ = − −
′′ = + −
′ =− −′′ − = − < ∈
−−
′′ =
→ +∞ ′′′ ≠′′ −
−−
•
−
− =
− + ⋅ ≠ + ⋅
•
−
− = −
− + ⋅ ≠ − + ⋅
•
( ) ( )( )
−
−
−
−
< > −
= + −
′ = − + −
′′ = + −′′′ = − + −
= + −
−
−− −
′ = = + ∈( )< > −= − ⋅ + −
−= + ⋅
−= − + +
′ =
−−
= − = −
−=
−=
−= ⋅
( )− − −
→∞ →∞ →∞⋅ = − ⋅ + = − + + =
−= ⋅
= − + + ≥
= +−
= ⋅
→
−−⋅=−
= + + +
′ = + +′′ = +
= == + + + == + + + =
′′ = + =
⇔ − ⇔ −− −
= − + +
=
= ⋅ =
= − = − + − −
− + − − =
− + + =
−− −
− −
( )− + + = − ⋅ − −
− − =
= + ≈
= − ≈ − ∉
≈
′ ′′= ∧ <′ = − + −′′ = − +
− + − =
− + =
= ± −
≈≈
′′ = − <′′ = >
=
= +
−= ⋅ = ⋅
−
→∞⋅ =
===⋅→∞→∞
−
→∞
= ∧ <
−
−
−
= ⋅ − −
′ = − ⋅ −
′′ = − ⋅
≈
′′ = − <≈
= − ∈ >⋅
•
•
•
•
•
•
• ∞
∈ �
{ }=
→ +∞ → −∞
≠
− = ⇔ = ⋅ ⇔ =⋅
− ⋅′ = +⋅
⋅′′ = −⋅
− ⋅′′′ = +⋅
′ = ≠
− ⋅ + = ⇔ = ⇔ =⋅
′′ =⋅
′′ >
−
′′ = ≠
⋅ − = ⇔ = ⇔ =⋅
→ +∞ −′′′ = ≠ ′′
−
-4 -2 2 4
-2
2
4
6
( ) ( )( ) ( )
− = − ⇔ − = −⋅ ⋅
⇔ ⋅ − = ⋅ −
⇔ ⋅ − = − ⋅ −
-4 -2 2 4
-2
2
= − −
= −
= − − −
= − − − − −
≈
→∞− − − − −
→∞− +
→ ∞
−
= ⋅ =
( )( )
= − = − = − = −⋅⋅⋅
−= − = − ⋅ = − ⋅
−
−−= + = −
−= + ⋅ ∈ ∈
=
∞
− = − + ⋅= + ⋅= + ⋅
⋅= + ⋅ ==
−= + ⋅
•
•
•
•
−= +
−
•
− − − − −= + ⋅ − − = + ⋅ ∈
− − − − −
•
− − −+ ⋅ = + ⋅
−
⋅ = −⋅ − ⋅ =⋅ − ⋅ = −
⋅ = −⋅ = −
−
•
= = −
− − −+ ⋅ = + ⋅
−
− − ⋅ = −+ ⋅ = + ⋅
− + ⋅ = + ⋅
= = −
•
α
= ≈ ≈ °⋅
α
⋅ + ⋅ =
−= − ⋅ ⇔ = − ⋅
−
+− = ⋅ +
→
∈ +
=− +
=
===
= = =
=−⋅− −
− −− = − −
− −
+ − −⋅ + ⋅ − − =
− −
⋅ ⋅ − + − ⋅ =− − = −
⋅ ⋅ + − ⋅ − ⋅ =+ =
− − − − − −⇔
− −
−
=→
−→
⋅−=
⋅ ⋅ = =
=→→
⋅−=
− −− − ⋅ = =− −
= =→→
⋅−=
→−
→⋅−=
− −− − ⋅ = =− −
− − =− + − =− − + =
⇔ =⇔ =⇔ =
= =
= =
→→⋅−= =
− −− = − −
− − − +
→− −
− − ⋅ = − − =− +− − − +
→→⋅=
[ ] ⋅ − − =− +
= − − +
′ = − +
′′ = −
′ ′′= ∧ <
( ) ( )
− + =
= ∨ = − ∉′′= <
−=
= − =
•
•
•
•
→
•μ
•
•
•
μ
−= = ⋅ ⋅ −
= = ≈
= = ⋅ ≈
= = ⋅ ⋅ ≈
= = ⋅ ⋅ ≈
= = ⋅ ⋅ ≈
≤ ≈
> = − ≤ ≈ − =
⋅
μ ⋅ ⋅
= ≈ ⋅μμ
= ≈ − = ≈
>
> = − ≤ ≈ − ≈
∞ ∞ ∞
= = =
⋅ ⋅ − ⋅ = ⋅ ⋅ ⋅ − ⋅ ⋅μ μ μμ μ μ
[ ]≈ ⋅ − − ⋅ − [ ]− ⋅ =
•
•
⋅ + ⋅ + ⋅ =
≤ ≤
−= = −
= ⋅ ⋅ −σ σ = ⋅ ⋅ = >
− −≤ ≤ ≈ Φ − Φ = ⋅ Φ −
≈ ⋅ Φ − ≈ ⋅ − = ≈
≤
=
μ = σ = ⋅ ⋅ ≈
μ σ≤ + ⋅ ≈≤ ≈ > ≈
≤≤ =μ σ = >
( )− +≤ ≈ Φ ≈ Φ ≈
[ ]
⋅ −− =
⋅ −
− ≤ ≥
⋅ − ⋅ − ≈
− ≤ ≈
⋅ −− = ⋅