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29 Cards in this Set

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Differentiation


d/dx sin x =

cos x

Differentiation


d/dx cos x

-sinx

Differentiation


f'n = 1+sinx-cosx

= cos x + sin x

tan x

= sin x /cos x

Product Rule

y' = Vu' + Uv'


where u = 1st Bracket


v = 2nd Bracket



Quotient Rule

y' = (Vu' - Uv')/ V^2


where u = top part


v = bottom part

Chain Rule

dy/dx = dy/du x du/dy

Pythagorus Theorem

y' = (Cos2 x + sin2 x)/ cos2 x


= 1/cos2 x

Anti-Differentiation


{ cos 4/3 x dx


= 3/4 sin 4/3x + c

Anti-Differentiation


y' = 3 sin 1/2 x



y = - 6 cos 1/2 x + c

Anti-Differentiation or Integration Cycle

sin --> -cos --> -sin --> cos --> sin

Differentiation Cycle

sin --> cos --> -sin --> - cos --> sin

Trapezoidal Rule:


Width of each strip

(b-a)/ n

Trapezoidal Rule:


Length of Integral

b - a

Bernoulli Trial :



There are only two possible answers


- as long as trials are independent

Bernoulli Trial :


Equation

p(success) + q(failure) = 1

Bernoulli Trial :


Equation 2

^n Cx . p^x . q ^n-x

Exponential and Log Functions: EQUATIONS

y= a^x




log,a, y = x

Exponential and Log Functions:


Q1 = -32 ^ 3/5

= -(2^5)^3/5


= - 2^3


= - 8

Exponential and Log Functions:


Q2 - 3^x = 243

Let 3^x = 3^5


Then x = 5

Exponential and Log Functions:


Q3 - 3^x = 15

(log15)/log 3


= 2.46 to 2.d.p

Laws and Properties:


= Log xy

= Log x + Log y

Laws and Properties:


Log x^n

= n Log x

Laws and Properties:


log 1

= 0

Laws and Properties:


log 10

= 1

Laws and Properties:


10 ^ logx

= x

Laws and Properties:


Log,a, x = log,a, y

--> x = y

Euler's Number:

f(x) = a^x, aER (Cannot Equal) 1

e = lim ( 1 - 1/n)^n


n--> Infinity


Euler's Number:


Q1 - 5^2x = e^y

log,e, 5^2x = log,e, e^y


2x log,e, 5 = y log,e, e


2x log,e, 5 = y


2x . 1.6094 = y


3.219x = y