M408D Midterm #1

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secx

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integrals to know

43 Terms

1

secx

ln| tanx + secx | +c

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2

integral of tanx

-ln |cosx| +c

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3

cosx

sinx

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4

sinx

-cosx

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5

what identity equals sec²x

1 + tan²x

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6

what identity equals csc²x

1 + cot²x

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7

what identity equals 1

cos²x + sin²x

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8

what is cot

1/tanx

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9

what csc

1/sinx

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10

what is sec

1/cosx

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11

half angle identity for sin²x

½(1-cos2x)

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12

half angle identity for cos²x

½(1+cos(2x))

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13

double angle identity for sin(2x)

2sinxcosx

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14

what is cosxsinx

2sin(2x) OR (sin²(x))/2

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15

integral of e^ 2x

e^(2x)/2

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16

integral of sqrt x

2x^(3/2) / 3

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17

integral of cos(pi * x)

sin(pix)/pi

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18

integral of ln(x)

xln(x) -x

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19

derivative of cos^-1

-1/sqrt (1-x²)

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20

integral of any regular fraction (ex: 5/4)

5x/4 (add x to numerator)

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21

integral of csc²x

-cot(x)

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22

integral of csc

-ln | cscx + cot(x) | +c

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23

integral of cotx

ln|sinx|+c

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24

what is sqrt (x²-a²)

asecx

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25

what is sqrt(a²-x²)

asinx

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26

what is sqrt(a²+x²)

atanx

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27

cos(2x)

2cos(x)²-1

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28

tan (x+y)=

tan(x) + tan(y)/1-tan(x)tan(y)

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29

sin (x/2)²

1-cos(x)/2

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30

cos(x/2)²

1+cos(x)/2

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31

sin (x + y)

sin(x)cos(y) + sin(y)cos(x)

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32

cos(x+y)

cos(x)cos(y) + sin(x)sin(y)

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33

cos and sin (pi/2)

(0,1)

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34

cos and sin (pi/4)

(sqrt2/2, sqrt2/2)

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35

cos and sin (pi)

(-1,0)

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36

cos and sin (pi/6)

(sqrt3/2, ½)

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37

cos and sin (3pi/2)

(0,-1)

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38

derivative of tanx

sec²x

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39

derivative of secx

tanxsecx

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40

derivative of cotx

-csc(x)²

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41

derivative of csc

-cotxcscx

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42

derivative of arcsin

1/sqrt(1-x²)

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43

derivative of arctan

1/1+x²

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