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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^2where 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-Differentiationy' = 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^xlog,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 = 3^5Then 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) 1e = 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, e2x log,e, 5 = y 2x . 1.6094 = y 3.219x = y