Equations Flashcards

1
Q

e^0

A

1

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2
Q

ln(e)

A

1

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3
Q

ln(1)

A

0

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4
Q

e^infinity

A

infinity

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5
Q

e^negative infinity

A

0

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6
Q

ln infinity

A

infinity

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7
Q

e^lnx

A

x

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8
Q

logx(x)^a

A

a

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9
Q

a^loga(y)

A

y

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10
Q

ln(e)^w

A

w

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11
Q

definition of the derivative

A

(f(x+h)-f(x))/h

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12
Q

second definition of the derivative

A

(f(x)-f(a))/x-a

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13
Q

chain rule derivative of f(g(X))

A

(f’(x)g(x))(g’(x))

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14
Q

f(x)=a^x, f’(x)=?

A

(a^x)((ln)a)

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15
Q

sinx domain and range

A

(-pi/2,pi/2), (-1,1)

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16
Q

arcsinx domain and range

A

(-1,1), (-pi/2,pi/2)

17
Q

cosx domain and range

A

(0, pi), (-1,1)

18
Q

arccos x domain and range

A

(-1,1), (0,pi)

19
Q

tanx domain and range

A

(-pi/2,pi/2), (-inf,inf)

20
Q

arctanx domain and range

A

(-inf,inf), (-pi/2,pi/2)

21
Q

lim (sinx/x)=

A

1

22
Q

lim (1-cosx/x)=

A

0

23
Q

sin(x+y)

A

sinxcosy + cosxsiny

24
Q

sin(x-y)

A

sinxcosy - cosxsiny

25
Q

1,2,rt3

A

pi/3,pi/6,90

26
Q

1, rt2, 1

A

pi/4,pi/4,90

27
Q

cos(x+y)

A

cosxcosy - sinxsiny

28
Q

cos(x-y)

A

cosxcosy + sinxsiny

29
Q

tan(x+y)

A

(tanx+tany)/(1-tanxtany)

30
Q

tan(x-y)

A

(tanx-tany)/(1+tanx+tany)

31
Q

sin2x

A

2sinxcosx

32
Q

cos2x

A

1-2sin^2

33
Q

tan2x

A

(2tanx)/(1-tan^2x)

34
Q

sin^2x

A

(1-cos2x)/2

35
Q

cos^2x

A

(1+cos2x)/2