Partial Fractions: Trig-Identities Arithmetic: Series: a , a + d , a + 2d , … a + d * (n - 1) , Where an + 1 = an + d, where d is the Common Difference an = a + d * (n - 1) Sumn = (a + an) * n / 2 Geometric: Series: a , ar , ar2 , … arn - 1 , Where an + 1 = an * r, where r is the Common Ratio an = ar n - 1 Sumn (if r != 1) = a1 (1 - r n) / (1 - r) Sumn (if r == 1) = a1 n Suminfinity (if -1 < r < 1) = a / (1 - r) Suminfinity (if -1 > r, or, r < 1) = impossible Binomial Theorem: Let nCr be n choose r, (a + b)n = nC0 * an b0 + nC1 * an - 1 b1 + nC2 * an - 2 b2 + … + nCn * a0 bn Generalized Binomial Theorem, -1 < x < 1: (1 + a)n = 1 + na + n(n - 1)/2! + n(n - 1)(n - 2)/3! + n(n - 1)(n - 2)(n - 3)/4! … Telescoping Series: Definition: a sum that goes to a fixed number. When asked, just expand then cancel out. Derivative: Tangent Line Chain Normal Line Where the tangent/normal intercepts the graph at point (a, f(a)) Where the tangent/normal intercepts the graph at point (a, f(a)) Product Quotient Linear Approx f(x) ~ f(a) + f’(a)(x-a) Where x is the closest approx and “a” is the real number Where u is upper and dv is lower. From this, integrate dv and differentiate u. Logarithmic Inverse Trigo Algebraic Trigo Exponential If the volume is V1 - V2, do integration separately Integral Note: int(ln(x)) = x * ln(x) - x (NOT SHOWN FOR SOME REASON) All in Positive Direction. Right hand. Note: during vector multiplication (a x b), index finger is (a), middle is (b), Thumb is result Use Scalar values for x and y (underlined) i + j + k + s(i + j + k) Results in Perpendicular Planes r ・n = a ・n, where “n” is the normal of the plane and “r” is the point where the normal starts and “a” is any other point on the plane. Note: if you see “ax + by + cz = C” This is translated to “r・(ai + bj + ck) = C” Line formed from Intersection of Planes