Uploaded by danat.kenzhegali03

Formula Sheet

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lif=28f-ce,col-of,
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literationof
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velength of CL)
13) (8)-+(81"of
L
=
-
tangent
t
fine to rc) at
e(t) F(a)
=
+
=
0.
5r(a)
2x
se d
e
fxy(a,b) fyx(a,b)
=
fxyy fyxy fyyx
=
=
Equation
of
plane:
a
Equation of
(F r0)
-
line:F (x)
a
*x >0: contours to the
by so:
are
contour value increase in
higher
positive y-direction
if you andcontoursarespreadingoutinpositivedirecto
30:
Eyy
right
0
=
To+at
=
and contours
if x30
and
if xco
exxto:
are
closer
contous to the
together
right
increation
right
further aport
to the
one
rordo
((f(x,y)dA ()f(rco,rina) dA=rolrdo
PoeEEEor
=
*
and
~
Griefetrhe
closed?
↓I
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No
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Can I find
=
of
clouds
orread
W
No
Independence
WefCB)f(A)
of
fxx(a,b)
> 0, fxx(a,b)
D
D3 0,
ECECH) for
or
D
the
of pants
and
8
=
Closing
ffd (F(rCH)
=
domain
ax-Py
rate
max
directional derivative
in the direction
=
=>
deftFit fitin
=
T0
=)
fxx+yy
<0
=>
local
local
-
((xy)-
min
max
raddle
inconclusive
=
of
max
increase
of f(x,y)
of change of t
Daf
measures
(xf11alc000
=
rate
of change
(xflw0
curlE =2Ry -Oz, Pz-Rx, Qx-Py]
ivF
d)
=
Px+Ory+RE
Equation of tangent plane:
(3D)
0
z-z)
*
F(X0,Yo, 50) (x- 40,y-yo,
b)(2D)
a) fy(a,b)(y
z f(a,b) + (x(a,b)(x
(to competein
=
-
y,07
-
-
+
=
positiveorientation
-
f(x,y) has horizontal tangent
ifRF 0
domain stay
in
=
achieves
Lagrange multipliers: Iff(x,y)to contraint
at (a,b) subject
global maximin
g(x,y) F, then D((a,p) 6DgC0,6)
=
=
the IFf(x,yhowlocalextremumotoTS
Iff(x,y)
domain,
0
=
direction
= 2P, 0, R):
<-EE)(x-x3
on
the
E
=1:
20.x7
It
is
Daf=ef.a
D:
SF. +CF.dF =fSQx-PyoA
When does
-
off
1411
in the
o
iP
<
The
Irctl
D
-
C0
&
worrtf dOFS
and
0
=
(9ax-PydA-F.o
Pothomiee
.
4f1ab1
=
integrals:
Vector line
Mass
If
derivative teet
bounded
continuous on closed +
absolute max and
then it achieve
that domain
min
plane
at
(40,30, f(x0,3)
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