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Flashcards in C3 Deck (71):
1

if y=eˣ, then x = ?

ln(y)

2

ln(a) + ln(b) = ?

ln(ab)

3

ln(a) - ln(b) = ?

ln(a/b)

4

kln(a) = ?

ln(aᵏ)

5

ln(e) = ?

1

6

ln(1) = ?

0

7

ln(eˣ) = ?

x

8

eˡⁿˣ = ?

x

9

lnx is the inverse of ?

10

eˣ is the inverse of ?

lnx

11

How do you display the root of two lines?

Intersection

12

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

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

13

What form must equations be in for iteration?

x =

14

What value should you first input into iteration?

lowest value of restriction range

15

How should you treat reflections?

As stretches

16

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

Doesn't matter

17

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

Stretch, then translate

18

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

Translate, then stretch

19

when does |x|= x?

when x≥0

20

when does |x| = -x?

when x≤0

21

If |x| = k, then x = ?

x = ±k

22

If |x| = |y| then x² =, x = ?

x² = y², x = ±y

23

Restrictions when |x| ≤ k

-k ≤ x ≤ k

24

Restrictions when |x| ≥ k

x ≥ k or x ≤ -k

25

If |𝓍| ≤ |y|, then 𝓍² ____ ?

𝓍² ≤ y²

26

y = eˣ, dy/d𝓍 = ?

dy/d𝓍 = eˣ

27

y = eᶠ⁽ˣ⁾, dy/d𝓍 = ?

dy/d𝓍 = f'(𝓍)eᶠ⁽ˣ⁾

28

y = ln𝓍, dy/d𝓍 = ?

dy/d𝓍 = 1/x

29

y = ln(f(𝓍)), dy/d𝓍 = ?

dy/d𝓍 = f'(x)/f(x)

30

y = [f(𝓍)]ⁿ, dy/d𝓍 = ?

dy/d𝓍 = nf'(x)[f(x)]ⁿ⁻¹

31

If y = u⋅v, then dy/d𝓍 = ?

dy/d𝓍 = vu' + uv'

32

If y = u/v, then dy/d𝓍 = ?

dy/d𝓍 = (vu' - uv')/v²

33

dy/d𝓍 x d𝓍/dy = ?

1

34

d𝓍/dy = ?

1/(dy/d𝓍)

35

cosec𝓍 = ?

1/sin𝓍

36

sec𝓍 = ?

1/cos𝓍

37

cot𝓍 = ?

1/tan𝓍 = cos𝓍/sin𝓍

38

CAST = ?

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

sin(A+B) = ?

sinAcosB + cosAsinB

40

sin(A-B) = ?

sinAcosB - cosAsinB

41

cos(A+B) = ?

cosAcosB - sinAsinB

42

cos(A-B) = ?

cosAcosB + sinAsinB

43

tan(A+B) = ?

(tanA + tanB)/(1 - tanAtanB)

44

tan(A-B) = ?

(tanA - tanB)/(1 + tanAtanB)

45

sin2A = ?

2sinAcosA

46

cos2A = ?

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

47

tan2A = ?

2tanA/(1 - tan²A)

48

sin4A = ?

2sin2Acos2A

49

asinθ + bcosθ can also be written as?

Rsin(θ±α) or Rcos(θ±α)

50

How do you write in the form Rcos(θ±α) from
Acos𝓍 - Bsin𝓍?

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

51

What does R give?

max/min value

52

tanA = ?

sinA/cosA

53

sin²A + cos²A = ?

1

54

secA = ?

1/cosA

55

cosecA = ?

1/sinA

56

cotA = ?

1/tanA = cosA/sinA

57

cosec²A = ?

1 + cot²A

58

sec²A = ?

tan²A + 1

59

∫eᶠ⁽ˣ⁾ d𝓍 = ?

eᶠ⁽ˣ⁾/f'(𝓍) + c

60

∫1/𝓍 d𝓍 = ?

ln|𝓍| + c

61

Reverse chain rule only works for?

Linear functions inside bracket

62

∫(a𝓍 + b)ⁿ d𝓍 = ?

1/(a(n+1) ⋅ (a𝓍 + b)ⁿ⁺¹ + c

63

∫f'(𝓍)/f(𝓍) d𝓍 = ?

ln|f(𝓍)| + c

64

∫n⋅f'(𝓍)/f(𝓍) d𝓍 = ?

n⋅ln|f(𝓍)| + c

65

Volume of revolution around the 𝓍 - axis?

Vₓ = π ᵇ∫ₐ [f(𝓍)]²

66

Volume of revolution around the y - axis?

Vᵧ = π ᵇ∫ₐ [g(y)]²

67

Volume of revolution between two curves?

Vₓ = π ᵇ∫ₐ [f(𝓍)]² - π ᵇ∫ₐ [g(𝓍)]²

68

Define: 𝓍∈R

𝓍 belongs to the set of real numbers

69

When are functions one-to-one?

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

70

How to find the vertex of a graph?

Complete the square
min/max point @ (-p,q)

71

Properties of Inverse functions

reflections in y=𝓍
only one-to-one functions have an inverse