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Trigonometricformulas

Differentiationformulas

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Integrationformulas

sin ( )y D A B x C = + AisamplitudeBistheaffectontheperiod(stretchorshrink)

Cisverticalshift(left/right)andDishorizontalshift(up/down)

Limits:

0 0

sin sin 1 coslim 1 lim 0 lim 0 x x x

x x x

x x x> > >

= = =

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ExponentialGrowthandDecay

kt y Ce=

RateofChangeofavariableyisproportionaltothevalueofy

'dy

ky or y kydx

= =

Formulasandtheorems

1.Afunctiony=f(x)iscontinuousatx=aif

i. f(a)exists

ii. exists,and

iii.

2. Evenandoddfunctions

1. Afunctiony=f(x)iseveniff(-x)=f(x)foreveryxinthefunction'sdomain.Everyevenfunctionissymmetricaboutthey-axis.

2. Afunctiony=f(x)isoddiff(-x)=f(x)foreveryxinthefunction'sdomain.Everyoddfunctionissymmetricabouttheorigin.

3. Horizontalandverticalasymptotes

1. Aliney=bisahorizontalasymptoteofthegraphofy=f(x)ifeither

or .

2. Alinex=aisaverticalasymptoteofthegraphofy=f(x)ifeither

or .

4.Definitionofaderivative

5. Tofindthemaximumandminimumvaluesofafunctiony=f(x),locate

1..thepointswheref'(x)iszeroorwheref'(x)failstoexist

2. theendpoints,ifany,onthedomainoff(x).

Note:Thesearetheonlycandidatesforthevalueofxwheref(x)mayhaveamaximumoraminimum

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6. Letfbedifferentiablefora

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