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29 Cards in this Set
- Front
- Back
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Differentiation d/dx sin x = |
cos x |
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Differentiation d/dx cos x |
-sinx |
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Differentiation f'n = 1+sinx-cosx |
= cos x + sin x |
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tan x |
= sin x /cos x |
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Product Rule |
y' = Vu' + Uv' where u = 1st Bracket v = 2nd Bracket |
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Quotient Rule |
y' = (Vu' - Uv')/ V^2 where u = top part v = bottom part |
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Chain Rule |
dy/dx = dy/du x du/dy |
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Pythagorus Theorem |
y' = (Cos2 x + sin2 x)/ cos2 x = 1/cos2 x |
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Anti-Differentiation { cos 4/3 x dx |
= 3/4 sin 4/3x + c |
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Anti-Differentiation y' = 3 sin 1/2 x |
y = - 6 cos 1/2 x + c |
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Anti-Differentiation or Integration Cycle |
sin --> -cos --> -sin --> cos --> sin |
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Differentiation Cycle |
sin --> cos --> -sin --> - cos --> sin |
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Trapezoidal Rule: Width of each strip |
(b-a)/ n |
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Trapezoidal Rule: Length of Integral |
b - a |
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Bernoulli Trial : |
There are only two possible answers - as long as trials are independent |
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Bernoulli Trial : Equation |
p(success) + q(failure) = 1 |
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Bernoulli Trial : Equation 2 |
^n Cx . p^x . q ^n-x |
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Exponential and Log Functions: EQUATIONS |
y= a^x log,a, y = x |
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Exponential and Log Functions: Q1 = -32 ^ 3/5 |
= -(2^5)^3/5 = - 2^3 = - 8 |
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Exponential and Log Functions: Q2 - 3^x = 243 |
Let 3^x = 3^5 Then x = 5 |
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Exponential and Log Functions: Q3 - 3^x = 15 |
(log15)/log 3 = 2.46 to 2.d.p |
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Laws and Properties: = Log xy |
= Log x + Log y |
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Laws and Properties: Log x^n |
= n Log x |
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Laws and Properties: log 1 |
= 0 |
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Laws and Properties: log 10 |
= 1 |
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Laws and Properties: 10 ^ logx |
= x |
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Laws and Properties: Log,a, x = log,a, y |
--> x = y |
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Euler's Number: |
f(x) = a^x, aER (Cannot Equal) 1
e = lim ( 1 - 1/n)^n n--> Infinity |
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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 |
