CALC - Memorize for the AP Calculus Test

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Y=f(x) must be continuous at each:

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39 Terms

1

Y=f(x) must be continuous at each:

-Critical Point or undefined and endpoints

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2

Local Minimum

Goes (-,0,+) or (-, und, +)

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3

Local Maximum

Goes (+,0,-) or (+, und, -)

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4

Point of Inflection

  • Concavity Changes

  • (+,0,-) or (-,0,+)

  • (+,und,-) or (-,und,+)

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5

D/dx(sinx)

Cosx

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6

D/dx(cosx)

-sinx

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7

D/dx(tanx)

SecĀ²x

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8

D/dx(cotx)

-cscĀ²x

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9

D/dx(secx)

Secxtanx

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10

D/dx(cscx)

-cscxcotx

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11

D/dx (lnx)

1/x Ɨ derivative of x

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12

D/dx(eāæ)

Eāæ derivative of n

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13

āˆ«Cosx

-Sinx

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14

āˆ«-sinx

Cosx

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15

āˆ«SecĀ²x

Tanx

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16

āˆ«-cscĀ²x

Cotx

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17

āˆ«Secxtanx

Secx

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18

āˆ«-cscxcotx

Cscx

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19

āˆ«1/n

Ln(n)

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20

āˆ«Eāæ

Eāæ

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21

When doing integrals never forget

Constant (+c)

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22

āˆ«Axāæ

A/n+1(xāæāŗĀ¹)+C

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23

āˆ«Tanx

  • Ln|secx|+c

  • -Ln|cosx|+c

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24

āˆ«Secx

Ln|secx+tanx|+c

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25

D/dx(sinā»Ā¹x)

1/āˆš1-xĀ²

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26

D/dx(cosā»Ā¹x)

-1/āˆš1-xĀ²

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27

D/dx(tanā»Ā¹x)

1/1+xĀ²

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28

D/dx(cotā»Ā¹x)

-1/1+xĀ²

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29

With derivative inverses

You plug in the number of the trigonometric function into x

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30

D/dx(secā»Ā¹x)

1/|x|āˆšxĀ²-1

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31

D/dx(cscā»Ā¹x)

-1/|x|āˆšxĀ²-1

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32

D/dx(aāæ)

aāæln(a)

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33

D/dx(Logā‚™x)

1/xln(a)

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34

Chain Rule

  • Take derivative of outside of parenthesis

  • Take derivative of inside parenthesis and keep the original of what was in the parenthesis

  • For example, sin(xĀ²+1)ā†’ 2xcos(xĀ²+1)

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35

Product Rule

d/dx first times second + first times d/dx second

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36

Quotient Rule

LoDHi-HiDLo/LoLo

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37

Fundamental Theorem of Calculus

  • āˆ«(a to b) f(x) dx = F(b) - F(a)

  • Basically saying that Fā€™(x)=f(x)

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38

fĀ relativeĀ maxā†’f ā€˜Ā goesĀ from

Positive to negative

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39

fĀ relativeĀ minā†’f ā€˜Ā goesĀ from

Negative to positive

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