pure Flashcards
tan^2, sec^2
1 + tan^2 = sec^2
cot^2, cosec^2
1 + cot^2 = cosec^2
Vieta quadratic equations
p+q = -b/a
pq = c/a
Vieta cubic equations
p+q+r = -b/a
pq + qr +pr = c/a
pqr = -d/a
derivative from 1st principes
lim h->0
f(x+h)−f(x) / h
cos differentiation
-sin
tan differentiation
sec^2
cot differentiation
-cosec
sec differentiation
sec x tan x
cosec differentiation
-cosec x cot x
even vs odd function
EVEN: f(-x) = f(x)
ODD: f(-x) = -f(x)
second derivative local min/max
local max if negative
local min if positive
parametric integration
x = f(t)
y = g(t)
to find new bounds plug in the x values and solve for t
integrate f’(t) g(t)
(differentiate x and leave y alone)
log rules
log(1) = 0
log(ab) = log(a) + log(b)
log(a/b) = log(a) - log(b)
log(a^n) = n log(a)
n
∑ 1
i= 1
n
∑ 1 = n
i= 1
n
∑ i
i= 1
n
∑ i = n(n+1)/2
i= 1
n
∑ i^2
i= 1
n
∑ i^2 = n(n+1)(2n+1)/6
i= 1
n
∑ i^3
i= 1
n
∑ i^3 = (n^2 (n+1)^2)/4
i= 1
n
∑ a+(i-1)d
i= 1
(arithmetic)
n
∑ a+(i-1)d = n/2(2a + (n-1)d)
i= 1
OR n/2(a1 + an)
where a1 is first term and an is last
n
∑ ar^i-1
i= 1
(geometric)
n
∑ ar^i-1=a(1-r^n)/1-r
i= 1
∞
∑ ar^i-1
i= 1
∞
∑ ar^i-1=a/1-r
i= 1
nth term of geometric series
an = ar^(n-1)
nth term of arithmetic series
an = a1 + (n-1)d
integral of ln(x)
x ln(x) - x
binomial expansion formula
(1+a)^n
1 + na +n(n-1)/2! a^2 + n(n-1)(n-2)/3!a^3 + …
turn (2+3x)^-3 into correct form
2^-3 (1+3x/2)^-3
partial fraction case
quadratic / (factor)(quadratic)
–>
A/factor + Bx+C/quadratic
integration by parts
∫AB = A∫B - ∫(A’∫B)
quotient rule
f’(x)g(x) - f(x)g’(x) / g(x) ^2
