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Elements of Calculus I (Math 1080) - Formula Sheet
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All the formulas from each module taught in MATH 1080 - Elements of Calculus I, taught at the University of Guelph. All hand-written notes.
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Formula SheetModule1-Reviewoffunc.to#.fC-x)--f( x ) Even Function
-
fl -
x) -
- -
fcx) Odd Function
-
PG) Cot C ,XtCzX2tCzX3t
-
-
. . . Polynomial Function
(4×227×7) ( ) slope Equation
'
y -
Yi = x -
X, Two -
point
Module2-Reviewoffunctions.fi
g) fcxltgcx
-
(
(x ) -_
) -
f -
g) ( x ) -_ fcx) -
gcx )
.
Cfg)Cx ) -
-
f- (x
)g( x )
(
Fg) ( x )=fCx)
lgcx ) (
fog
)Cxl=
fcgcx ))
-
.
Module3-Reviewoflogi.Exponentialfunc.to#.1ogbCxI=ylogblbw
'
Incx ) -
-
y iff e'
iff
'
bY=x
=
X
-
.
b'09kW
In ( eu)=W
)
-
W -
'
e'
new
)=w
) -
-
W
.
-
In (e)
logb(b) =/
= I
"
ACH -_
Aoe Exponential Growth Equation
-
Alt) kt= >
Exponential Decay Equation
Aoe
-
- -
-
-
Actin)=tzAo= > Half Life -
Module4-Reviewoftrig-Funch.co#-si
) nCx)--SinCxt2nTl -
cos (x ) = (Xt 2nF )
.
Sin C- x ) = -
sink) (since sincxlisodd) .
cost -
x)
-
-
Cosa ) ( since coscxliseven)
-
sin2xtcosx-l.lt/-znZCx)=Sec2Cx) -
I + cot2( x ) -
-
Csa ( x )
4maxz-ymin-ip-2.IM/ib=Ym2xzt4min-
-
k=
Module5-Modelldentificah
y=cxk
log (y ) klogcxltlogcc )
- -
-
logcyzl-logcyiloglx
l og.kz
k=
-
) -
. )
Module6-Discretemodelli ng-sequences.se#.E2n3+nFiI'
Ieermmtotostosfaattat .
anti =2ntd -
an -
- aitch 1) d-
gn rn
'
fnt2=fn+ , t Fn
grit , =rgn
-
g
- ' i
-_
,
NI ( an bn) KI ,2n= Is Kan
'
±
-
an bn = '
, . ,
I. han II. I II ,k=Nk II ,n=NCNz
' '
-
-
an
-
an
, II NCNtly.HN#n&.,n3=N2CNtl)Z-
'
nZ=
,
I. grn =gCi I.ms/rY#n)
'
'
'
-
'
IEM ( anti -
2n) =
anti -
2M
-
FIM (an -
In -
1) =
IN -
IM - I
Module7-i-Dif erenceEqus.to#-AXn=Xntl-Xn-Xntl=Xntb Xn =
Xotnb if 2=1
'
Xntl -
-
2Xn = > Xn =
Xo an if b O -
-
(
Xntl=2Xntb if 2 # I
#
'
=3
xn = + Xo -
an
{
hi ? ( d)
b) I 2 if I < act Xo 41-2=0
'
or
- -
-
a
+
Xo -
+
*
+ so
if a> I Xo -
blt -
a > O
I
=
-
a
if a> ,
Xo -
bh -
a
< O
DNE if a E -
I ,
Xo -
41 -
a # O
{
if b > O
thin?
'
+ a
Xotnb = >
I =
- a
if b< O
Xo if b=O
-
Xe -
- f- (XE) Equilibrium State
Module8-Limitsandconh.nu#
lixhfafcx) =L iff
tix?fz fcxl
tiffs
-
.
= fcx) =L
.
↳ LH limit ↳
RH limit
lixhfakfcx) yzfCx )
'
= k ) k is a constant
tix? Cfcxltgcx )) finna fan
tixhfagcx)
-
=
±
,
xlihfzflxlgcx ) ( lixnzfcxl ) ( tix? gcxl )
-
-
-
,
?fa(§,)=
limx-safcxil mx-sagcxl. i?fzCfog7Cxl- lixMsafCgCxl =f(
tix
'
fifa gcx ) ) =
fcgca) ) when continuous
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