Unit 1 Flashcards
rational function
f(x) = P(x)/Q(x)
- P(x) and Q(x) are polynomials
inverse
- a function has a ____ only if it is one-one
- use horizontal line test (if one output has two inputs, it doesn’t have an inverse) - a function and its _____ are symmetric over y=x
LOG PROPERTIES
log(b) 1 =
0
log(b) b =
1
log(b) m^n =
nlog(b) m
log(b) a • log(c) a =
log(c) b
log(b) a = log(b) c means
a = c
b^[log(b) x] =
x
log(b) a =
log(a)/log(b)
NATURAL LOG PROPERTIES
ln(ab) =
ln(a) - ln(b)
ln(a/b) =
ln(a) - ln(b)
ln(a^2) =
2ln(a)
ln(1) =
0
ln(e) =
1
POLAR FUNCTIONS
polar function
defines a curve with an equation of the form r = f(θ)
- (r, θ)
to find what values of θ the function passes through the origin:
set function equal to 0
to find when two polar graphs intersect:
set their equations equal to each other
- polar form
polar functions can be written parametrically:
x = rcosθ
y = rsinθ
to find the slope of r = f(θ), first express curve in parametric form
if f(θ) is differentiable, then so are x and y. Use:
dy/dx = (dy/dθ)/(dx/dθ)
= (r’sinθ + rcosθ)/(r’cosθ - rsinθ)
polar area of one curve =
a
1/2 ∫ [r(θ)]^2 dθ
b
Polar area between curves
- find at what θ the graphs intersect
a A = 1/2 ∫ (Outer^2 - Inner^2)dθ b - if you were to draw a line at θ within the area being calculated, there would be a line closer to the point of origin than the other
