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CIV109 - Mathematics and Python Programming > Functions > Flashcards

Functions Flashcards

1
Q

What does [ mean?

A

the number can go up to and include

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2
Q

What does ( mean?

A

the number can go up to but not include it

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3
Q

What is an even function?

A

f(-x) = f(x)

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4
Q

What does an even function look like?

A
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5
Q

What is an odd function?

A

f(-x) = -f(x)

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6
Q

What does an odd function look like?

A
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7
Q

What is a periodic function?

A

f(t + nT)

y = f(t) if there is a number T, such that f(t + nT) = f(t), all integers n then f(t) is periodic.

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8
Q

What does a continuous function look like?

A
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9
Q

What does a discontinuous function look like?

A
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10
Q

What does a discontinuous function look like?

A
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11
Q

How do you convert from degrees to radians?

A

x pi/180

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12
Q

How do you convert from radians to degrees?

A

x 180/pi

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13
Q

what period does y = cosθ have?

A

2*pi

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14
Q

Is y = cosθ an ODD, EVEN or neither function?

A

Even

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15
Q

What period does y = sinθ have?

A

2*pi

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16
Q

What function is y = sinθ EVEN, ODD or neither?

A

Odd

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17
Q

What period does y = tanθ have?

A

2*pi

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18
Q

What period does y = tanθ have?

A

2*pi

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19
Q

What function does y = tanθ EVEN, ODD or neither?

A

ODD

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20
Q

What is the identity that includes cos^2(θ) and sin^2(θ)?

A

cos^2(θ) + sin^2(θ) = 1

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21
Q

What does cos(a + b) =

A

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

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22
Q

What does cos(a + b) =

A

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

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23
Q

What does cos(a - b) =

A

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

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24
Q

What does sin(a + b) =

A

sin(a + b) = sin(a)cos(b) + sin(b)cos(a)

25
Q

what does sin(a - b) =

A

sin(a - b) = sin(a)cos(b) - sin(b)cos(a)

26
Q

what is the equation for binomial expansion?

A
27
Q
A
28
Q

what is the equation for the generalised binomial coefficients?

A
29
Q

given f, find f^(-1)?

A

put y = f(x)
solve for x

30
Q

find the inverse function for y = sinθ?

A
31
Q

find the inverse function for y = sinθ?

A
32
Q

find the inverse function for y = sinθ?

A
33
Q

What does the graph for y = arccosθ look like?

A
34
Q

What does the graph for y = arccosθ look like?

A
35
Q

What does the graph for y = arctanθ look like?

A
36
Q

what does e^x differentiate to?

A

e^x

37
Q

What does the graph e^x look like?

A
38
Q

What does the graph y = ln(x) look like?

A
39
Q

ln(e^x) =

A

x

40
Q

e^ln(x) =

A

x

41
Q

ln(xy) =

A

ln(xy) = ln(x) + ln(y)

42
Q

ln(x/y) =

A

ln(x/y) = ln(x) - ln(y)

43
Q

ln(x^p) =

A

p*ln(x)

44
Q

what does ln(x) differentiate to?

A

1/x

45
Q

a^x = y <=>

A

log_a(y)

46
Q

What is sinh(x) =

A

sinh(x) = 1/2*(e^x - e^(-x))

47
Q

What is cosh(x)?

A

cosh(x) = 1/2*(e^x + e^(-x))

48
Q

What is tanh(x)?

A

tanh(x) = sinh(x)/cosh(x)

49
Q

What does the graph for sinh(x) look like?

A
50
Q

What does the graph for cosh(x) look like?

A
51
Q

What does the graph for tanh(x) look like?

A
52
Q

What is the identity that links cosh(x) and sinh(x)?

A

cosh^2(x) - sinh^2(x) = 1

53
Q

what does cosh(a + b) =

A

cosh(a + b) = cosh(a)cosh(b) + sinh(a)sinh(b)

54
Q

What does cosh(2x) =

A

cosh(2x) = cosh^2(x) + sinh^2(x)

55
Q

what does sinh(a + b) =

A

sinh(a + b) = cosh(a)sinh(b) + sinh(a)cosh(b)

56
Q

what does sinh(2x) =

A

sinh(2x) = 2sinh(x)cosh(x)

57
Q

what does sinh(x) differentiate into?

A

cosh(x)

58
Q

What does cosh(x) differentiate into?

A

sinh(x)

CIV109 - Mathematics and Python Programming (3 decks)

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