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