Formulae not in booklets Flashcards
The area of a histogram box is proportional to
frequency
Area of a histogram box=
k x frequency
The frequency of a histogram box is proportional to
Frequency density x class width
Frequency density=
k x frequency/ class width
or
area/ class width
What are the formulae for the energy stored in a spring/ string/ rod?
= 1/2 x force x extension
= 1/2 x k x extension^2
= 1/2 x force^2/ k
Area of integration
Between limits x1 to x2 integrate (y(x))dx
Derivative of tanx
sec^2(x)
Integral of tanx
ln|sec(x)| + c
Derivative of sinx
Cosx
Integral of sinx
-(- cosx)
Derivative of secx
sec(x)tan(x)
Arithmetic series
Sn= n/2 (2a + (n-1)d) or
Sn= n/2(a+l)
Nth term of a geometric sequence
Un= ar^(n-1) where r= common ratio
Geometric series
Sn= a(1-r^n)/ 1-r or
Sn= a(r^n- 1)/ r-1
A geometric sequence is convergent if….
|r|<1
Sum of a convergent geometric series
S(infinity)= a/(1-r)
How do you know if a sequence is increasing or decreasing
Increasing: Un+1>Un
Decreasing: Un+1<Un
For all natural numbers
How do you know if a sequence is periodic
Un+k= Un
Where k is the order of the sequence
Interpolation formula e.g. Q1
Q1= value until interval + (difference between first and nth interval)/ (difference between first and last number in interval) × class width
Integral of secx
secx x tanx
