C3 Flashcards

1
Q

if y=eˣ, then x = ?

A

ln(y)

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2
Q

ln(a) + ln(b) = ?

A

ln(ab)

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3
Q

ln(a) - ln(b) = ?

A

ln(a/b)

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4
Q

kln(a) = ?

A

ln(aᵏ)

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5
Q

ln(e) = ?

A

1

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6
Q

ln(1) = ?

A

0

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7
Q

ln(eˣ) = ?

A

x

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8
Q

eˡⁿˣ = ?

A

x

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9
Q

lnx is the inverse of ?

A

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10
Q

eˣ is the inverse of ?

A

lnx

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11
Q

How do you display the root of two lines?

A

Intersection

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12
Q

How do you show that a root lies between 4 & 5?

A

input x=4 into f(x)
input x=5 into f(x)
if there is a sign change then root lies between the two values of x

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13
Q

What form must equations be in for iteration?

A

x =

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14
Q

What value should you first input into iteration?

A

lowest value of restriction range

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15
Q

How should you treat reflections?

A

As stretches

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16
Q

If stretches & translations are in different axes, then the order ____ ?

A

Doesn’t matter

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17
Q

If stretches & translations are both in the y axes, then the order ____ ?

A

Stretch, then translate

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18
Q

If stretches & translations are both in the x axes, then the order ____ ?

A

Translate, then stretch

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19
Q

when does |x|= x?

A

when x≥0

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20
Q

when does |x| = -x?

A

when x≤0

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21
Q

If |x| = k, then x = ?

A

x = ±k

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22
Q

If |x| = |y| then x² =, x = ?

A

x² = y², x = ±y

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23
Q

Restrictions when |x| ≤ k

A

-k ≤ x ≤ k

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24
Q

Restrictions when |x| ≥ k

A

x ≥ k or x ≤ -k

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25
Q

If |𝓍| ≤ |y|, then 𝓍² ____ ?

A

𝓍² ≤ y²

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26
Q

y = eˣ, dy/d𝓍 = ?

A

dy/d𝓍 = eˣ

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27
Q

y = eᶠ⁽ˣ⁾, dy/d𝓍 = ?

A

dy/d𝓍 = f’(𝓍)eᶠ⁽ˣ⁾

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28
Q

y = ln𝓍, dy/d𝓍 = ?

A

dy/d𝓍 = 1/x

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29
Q

y = ln(f(𝓍)), dy/d𝓍 = ?

A

dy/d𝓍 = f’(x)/f(x)

30
Q

y = [f(𝓍)]ⁿ, dy/d𝓍 = ?

A

dy/d𝓍 = nf’(x)[f(x)]ⁿ⁻¹

31
Q

If y = u⋅v, then dy/d𝓍 = ?

A

dy/d𝓍 = vu’ + uv’

32
Q

If y = u/v, then dy/d𝓍 = ?

A

dy/d𝓍 = (vu’ - uv’)/v²

33
Q

dy/d𝓍 x d𝓍/dy = ?

A

1

34
Q

d𝓍/dy = ?

A

1/(dy/d𝓍)

35
Q

cosec𝓍 = ?

A

1/sin𝓍

36
Q

sec𝓍 = ?

A

1/cos𝓍

37
Q

cot𝓍 = ?

A

1/tan𝓍 = cos𝓍/sin𝓍

38
Q

CAST = ?

A

C - only cosine is positive (270-360) (repeats at 360-α)
A - All trig are positive (0-90)
S - only sine is positive (90-180) (repeats at 180-α)
T - only tan is positive (180-270) (repeats at 180+α)

39
Q

sin(A+B) = ?

A

sinAcosB + cosAsinB

40
Q

sin(A-B) = ?

A

sinAcosB - cosAsinB

41
Q

cos(A+B) = ?

A

cosAcosB - sinAsinB

42
Q

cos(A-B) = ?

A

cosAcosB + sinAsinB

43
Q

tan(A+B) = ?

A

(tanA + tanB)/(1 - tanAtanB)

44
Q

tan(A-B) = ?

A

(tanA - tanB)/(1 + tanAtanB)

45
Q

sin2A = ?

A

2sinAcosA

46
Q

cos2A = ?

A

= cos²A - sin²A
= 1 - 2sin²A
= 2cos²A - 1

47
Q

tan2A = ?

A

2tanA/(1 - tan²A)

48
Q

sin4A = ?

A

2sin2Acos2A

49
Q

asinθ + bcosθ can also be written as?

A

Rsin(θ±α) or Rcos(θ±α)

50
Q

How do you write in the form Rcos(θ±α) from

Acos𝓍 - Bsin𝓍?

A
Equate cos𝓍 & sin𝓍 terms so 
Rcosα = A & Rsinα = B
∴ tanα = B/A
R² = A² + B²
R = √(A² + B²)
51
Q

What does R give?

A

max/min value

52
Q

tanA = ?

A

sinA/cosA

53
Q

sin²A + cos²A = ?

A

1

54
Q

secA = ?

A

1/cosA

55
Q

cosecA = ?

A

1/sinA

56
Q

cotA = ?

A

1/tanA = cosA/sinA

57
Q

cosec²A = ?

A

1 + cot²A

58
Q

sec²A = ?

A

tan²A + 1

59
Q

∫eᶠ⁽ˣ⁾ d𝓍 = ?

A

eᶠ⁽ˣ⁾/f’(𝓍) + c

60
Q

∫1/𝓍 d𝓍 = ?

A

ln|𝓍| + c

61
Q

Reverse chain rule only works for?

A

Linear functions inside bracket

62
Q

∫(a𝓍 + b)ⁿ d𝓍 = ?

A

1/(a(n+1) ⋅ (a𝓍 + b)ⁿ⁺¹ + c

63
Q

∫f’(𝓍)/f(𝓍) d𝓍 = ?

A

ln|f(𝓍)| + c

64
Q

∫n⋅f’(𝓍)/f(𝓍) d𝓍 = ?

A

n⋅ln|f(𝓍)| + c

65
Q

Volume of revolution around the 𝓍 - axis?

A

Vₓ = π ᵇ∫ₐ [f(𝓍)]²

66
Q

Volume of revolution around the y - axis?

A

Vᵧ = π ᵇ∫ₐ [g(y)]²

67
Q

Volume of revolution between two curves?

A

Vₓ = π ᵇ∫ₐ [f(𝓍)]² - π ᵇ∫ₐ [g(𝓍)]²

68
Q

Define: 𝓍∈R

A

𝓍 belongs to the set of real numbers

69
Q

When are functions one-to-one?

A

When each member of 𝓍 maps to only one member of y

70
Q

How to find the vertex of a graph?

A

Complete the square

min/max point @ (-p,q)

71
Q

Properties of Inverse functions

A

reflections in y=𝓍

only one-to-one functions have an inverse