Basics to Learn Flashcards
1
Q
derivative of cos
A
-sinx
2
Q
derivative of sin
A
cosx
3
Q
an integral of cos
A
sinx
4
Q
an integral of sin
A
-cosx
5
Q
sin(π/6)
A
1/2
6
Q
sin(π/4)
A
√2/2
7
Q
sin(π/3)
A
√3/2
8
Q
cos(π/6)
A
√3/2
9
Q
cos(π/4)
A
√2/2
10
Q
cos(π/3)
A
1/2
11
Q
tan(π/6)
A
√3/3
12
Q
tan(π/4)
A
1
13
Q
tan(π/3)
A
√3
14
Q
chain rule f(g(x))
A
g’(x) f’(g(x))
15
Q
product rule
A
(uv)’ = u’v + uv’
16
Q
Quotient rule
A
(u/v)’ = u’v - uv’ / v^2
17
Q
finding the area between two curves
A
∫ᵇₐ(function of top curve - function of bottom curve)dx
18
Q
integral of sec²x
A
tanx
19
Q
integral of eᵏˣ
A
1/keᵏˣ
20
Q
integral of 1/x
A
ln|x|
21
Q
integral of f’(x)/f(x)
A
ln|f(x)|+c
22
Q
sin cos identity
A
sin²x+cox²x=1
23
Q
sec tan identity
A
sec²x=1+tan²x
24
Q
cot cosec identity
A
1 + cot²x = cosec²x
25
sin(2x)
2sin(x)cos(x)
26
cos(2x) =
cos²x-sin²x
27
tan(a+b)
tana+tanb/1-tanatanb
28
y = f(x) + a
translates a in the y direction
29
y = f(x+a)
translates -a in the x direction
30
y = af(x)
stretch SF a in y direction
31
y = f(ax)
stretch of 1/a in x direction
32
y = -f(x)
reflection in x axis
33
y = f(-x)
reflection in y axis
34
limit as x tend to 0 of sinx/x
1
35
limit as x tends to 0 of (1-cosx)/x²
1/2
36
limit as x tends to infinity of (1+1/x)²
e
37
limit as x tends to minus infinity of (1+1/x)²
e
38
limit as x tends to 0 of (1+x)¹/ˣ
e
39
limit as x tends to 0 of (log(1+x))/x
1
40
limit as x tends to 0 of (eˣ-1)/x
1
41
limit as x tends to infinity eˣ/xᵇ
infinity (for all b>0)
42
limits as x tends to infinity logx/xᵇ
0
43
limit as x tends to 0 from the right of xᵇlogx
0
44
L'Hopitals Rule
Let a,b,c∈ℝ such that a≤b≤c and a!=b. Let Ω = (a,b)\{c}. Let f,g: Ω -> ℝ be differentiable functions such that g'(x)!=0 for all x∈Ω. Assume that one of the following conditions holds:
(i) limit as x tends to c of f(x) = 0 and limit as x tends to c of g(x) = 0
(ii) limits as x tends to c of f(x) = +- infinity and limit as x tends to c of g(x) = +- infinity
