precalc final

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50 Terms

1
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y=sinx

domain: (-∞, ∞)
Range: [-1, 1]

Period: 2π

x-int: πk

max: (π/2)+2πk

min: (3π/2)+2πk

Derivative: y1=cosx

<p>domain: (-<span>∞, ∞)</span><br><span>Range: [-1, 1]</span></p><p><span>Period: 2</span>π</p><p>x-int: πk</p><p>max: (π/2)+2πk</p><p>min: (3π/2)+2πk</p><p>Derivative: y<sup>1</sup>=cosx</p>
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y=cosx

domain: (-∞, ∞)
Range: [-1, 1]

Period: 2π

x-int: (π/2)+πk

max: 2πk

min: π+2πk

Derivative: y1=-sinx

<p>domain: (-∞, ∞)<br>Range: [-1, 1]</p><p>Period: 2π</p><p>x-int: (π/2)+πk</p><p>max: 2πk</p><p>min: π+2πk</p><p>Derivative: y<sup>1</sup>=-sinx</p>
3
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y=tanx

domain: R except (π/2)+2πk

Range: (-∞, ∞)

x-int: x=πk

derivative: sec2x

asymptotes: x = π/2 + πk

<p>domain: R except (π/2)+2πk</p><p>Range: (-∞, ∞)</p><p>x-int: x=πk</p><p>derivative: sec<sup>2</sup>x</p><p>asymptotes: x = π/2 + πk</p>
4
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y=sin-1x

inputs of y-coordinates on the unit circle, outputs of angles between [-π/2, π/2]

domain: [-1, 1]

range: [-π/2, π/2]

<p>inputs of y-coordinates on the unit circle, outputs of angles between [-π/2, π/2]</p><p>domain: [-1, 1]</p><p>range: [-π/2, π/2]</p>
5
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y=cos-1x

inputs of x-coordinates on the unit circle, outputs of angles between [0, π]

domain: [-1, 1]

range: [0, π]

<p>inputs of x-coordinates on the unit circle, outputs of angles between [0, π]</p><p>domain: [-1, 1]</p><p>range: [0, π]</p>
6
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y=tan-1x

inputs of slopes on the unit circle, outputs of angles between (-π/2, π/2)

domain: (-∞, ∞)

range: (-π/2, π/2)

<p>inputs of slopes on the unit circle, outputs of angles between (-π/2, π/2)</p><p>domain: (-∞, ∞)</p><p>range: (-π/2, π/2)</p>
7
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y=cscx

cscθ=1/sinθ

sinθ=1/cscθ

domain: R except x=π/k

range: (-∞, -1] U [1, ∞)

period: 2π

<p>cscθ=1/sinθ</p><p>sinθ=1/cscθ</p><p>domain: R except x=π/k</p><p>range: (-∞, -1] U [1, ∞)</p><p>period: 2π</p>
8
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y=secx

secθ=1/cosθ

cosθ=1/secθ

domain: R except x=π/2+πk

range: (-∞, -1] U [1, ∞)

period: 2π

<p>secθ=1/cosθ</p><p>cosθ=1/secθ</p><p>domain: R except x=π/2+πk</p><p>range: (-∞, -1] U [1, ∞)</p><p>period: 2π</p>
9
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y=cotx

cotθ=1/tanθ=cosθ/sinθ

tanθ=1/cotθ=sinθ/cosθ

domain: R except x=πk

range: (-∞, ∞)

period: π

asymptotes: πk

<p>cotθ=1/tanθ=cosθ/sinθ</p><p>tanθ=1/cotθ=sinθ/cosθ</p><p>domain: R except x=πk</p><p>range: (-∞, ∞)</p><p>period: π</p><p>asymptotes: <span>πk</span></p>
10
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Sinusoids

y=Asin(b(x-c))+D

y=Acos(b(x-c))+D

amplitude: |A| — vertical stretch/displacement, distance from midline to max or min

vertical displacement: D — vertical shift (average of max or min)

period: 2π/b — horizontal stretch, compression

phase shift: c — horizontal shift

11
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y=ex

knowt flashcard image
12
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y=lnx

knowt flashcard image
13
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odd function

symmetric around origin

f(-x)=-f(x)

14
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even function

symmetric over y-axis

f(x)=f(-x)

15
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eccentricity

PF/Pd=1 (parabola)

0<PF/Pd<1 (ellipse)

PF/Pd>1 (hyperbola)

e=c/a

16
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continuity calc definition

f(c) exists

lim(x→c) of f(x) exists

lim(x→c) of f(x) = f(c)

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remainder theorem

if a polynomial function, f, is divided by (x - a), then the remainder is f(a).

18
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factor theorem

if (x - a) divides a polynomial function, f, evenly, then f(a) = 0.

possible zeros are +- factors of the leading coefficent over the constant

19
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slope of a tangent line

 f'(c)=lim(x→c) = f(x)-f(c)/x-c

20
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rational function asymptote

y=0 when the degree of q > the degree of p

y=a/b when the degree of q = the degree of p
(where a = leading coefficient of p and b = leading coefficient of q)

slant asymptote when the degree of q < the degree of p

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rational function slant asymptote

divide function

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logbc

logac/logab

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logbxy

logbx+logby

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logb(x/y)

logbx-logby

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logbxy

y(logbx)

26
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SAS Area

A=1/2*a*b*sinC

27
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Law of sines

a/sinA=b/sinB=c/sinC

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Law of cosines

a2=b2+c2-2bc*cosA

29
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Pythagorean IDs

sin2θ+cos2θ=1

csc2θ-cot2θ=1

sec2θ-tan2θ=1

30
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Even/Odd IDs

sin(-x)=-sin(x)

cos(-x)=cosx

tan(-x)=-tan(x)

31
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Co-Function IDs

sin(90-θ)=cosθ, cos(90-θ)=sinθ

sec(90-θ)=cscθ, csc(90-θ)=secθ

cot(90-θ)=tanθ, tan(90-θ)=cotθ

32
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sin(A+B)

sinAcosB+sinBcosA

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cos(A+B)

cosAcosB-sinAsinB

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tan(A+B)

(tanA+tanB)/1-tanAtanB

35
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sin(2x)

2sinxcosx

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cos(2x)

cos2x-sin2x

1-2sin2x

2cos2x-1

37
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acisα*bcisβ

abcis(α+β)

38
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(rcisθ)n

rncis(n*θ)

39
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derivative of xn (power rule)

n*xn-1

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derivative of ex

ex

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derivative of ebx

b*ebx

42
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derivative of bx

lnb*bx

43
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derivative of ln(x)

1/x

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derivative of logbx

1/x*ln(b)

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derivative of sinx

cosx

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derivative of cosx

-sinx

47
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limit definition of a derivative at a point

lim(h→0) (f(x+h)-f(x))/h

48
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combinations

n!/(n-k)!k!

added k b/c order doesnt matter, get rid of repeats

49
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permutations

n!/(n-k!)

50
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tan2x

2tanx/(1-tanx)