LIMITS
eg D
first
simplify
eg sling E eg sting5 3
p as É 13T denominatanaged
3
BEE.isntose i limitdoesnotexist
5 Ims bS
GRADIENTS
Straightline constantm Curvedline averagembetween2puts
usewhen2priesaregiven
m 1
m increasingfunction
egfloc set3x
m decreasingfunction averagegradientoff x between x
Determinethe 1and x 2
m o horizontalline
4 6
ñ
AVERAGERATEOFCHANGE
In agraphmeasuringdistancetraveledagainsttime averagegradientgivesaveragevelocity T Ee
theaveragespeed
fappiffidetermine
I
w
̅ timeIs
, TANGENTTOCURVE
in thhh.tn
I
npgieetaahadisaiaierbptieen
Gradientofa tangent
Mi Ling Lee ignetataspecific
gigthen999
eg Findtheequationofthetangenttotheparabolay x atso
m hing
Em FindMt
Findgvalueof x putgiven
n'To th
subsintoyy mlocsadtofindequation
IhI
110 pinto I
2
DERIVATIVE
thegradientofthetangentat apoint
thelimitoftheaveragegradient if h o
theinstantaneousrate ofchangeof floc withrespectto x at a specificpoint
Notation whenfloc isderived itbecomes acos
when isderived itbecomes
y or 1 y
Firstprinciplesformula f x fl
himfathy
2
eg findthederivativeoffloc 2 500usingfirstprinciples
I IE
4 5 gradient 2002
500
off
egHence findF 2
f2 2 5
334
eg D
first
simplify
eg sling E eg sting5 3
p as É 13T denominatanaged
3
BEE.isntose i limitdoesnotexist
5 Ims bS
GRADIENTS
Straightline constantm Curvedline averagembetween2puts
usewhen2priesaregiven
m 1
m increasingfunction
egfloc set3x
m decreasingfunction averagegradientoff x between x
Determinethe 1and x 2
m o horizontalline
4 6
ñ
AVERAGERATEOFCHANGE
In agraphmeasuringdistancetraveledagainsttime averagegradientgivesaveragevelocity T Ee
theaveragespeed
fappiffidetermine
I
w
̅ timeIs
, TANGENTTOCURVE
in thhh.tn
I
npgieetaahadisaiaierbptieen
Gradientofa tangent
Mi Ling Lee ignetataspecific
gigthen999
eg Findtheequationofthetangenttotheparabolay x atso
m hing
Em FindMt
Findgvalueof x putgiven
n'To th
subsintoyy mlocsadtofindequation
IhI
110 pinto I
2
DERIVATIVE
thegradientofthetangentat apoint
thelimitoftheaveragegradient if h o
theinstantaneousrate ofchangeof floc withrespectto x at a specificpoint
Notation whenfloc isderived itbecomes acos
when isderived itbecomes
y or 1 y
Firstprinciplesformula f x fl
himfathy
2
eg findthederivativeoffloc 2 500usingfirstprinciples
I IE
4 5 gradient 2002
500
off
egHence findF 2
f2 2 5
334
