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Elements of Calculus I (Math 1080) - Formula Sheet

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Course
MATH 1080 (MATH1080)

Institution
University Of Guelph (U Of G )

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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Uploaded on December 13, 2019
Number of pages 5
Written in 2019/2020
Type Other
Person Nagham mohammed

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calculus
formulas
math 1080
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Formula Sheet
Module1-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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