Week 1 Functions in Cartesian and Polar Coordinates Flashcards
describe a cartesian coordinate system
Coordinate system that has a perpendicular axis system
describe a polar coordinate system
circular coordinate system that tells you the distance from the origin and the angle wrt a pre defined axis
what is the range of a function
output values
what is the domain of a function
input values of a function
what are the zeros of a function
the input values that give an output value of 0
what is the intercept of a function
the output value when the input value is 0
define an even function
function that has mirror symmetry so f(x) = f(-x)
define an odd function
function that is antisymmetric so f(x) = -f(-x)
what 7 things must be considered when drawing a cartesian function
Range and Domain Zeros and Intercepts Sign of the function Symmetries Behaviour at infinity and asymptotes Maxima and Minima (first derivative) Curvature (second derivative)
when is it easier to use polar coordinates
for functions with circular symmetry
what are the two components of a polar coordinate system
r the radial distance from the origin
θ the anticlockwise angle from the axis
give the 4 polar/cartesian conversion equations
r = sqrt( x^2 + y^2 ) θ = arctan (y/x) x = rcosθ y = rsinθ
what is the special property of the exponential function e
it is its own derivative
give the 5 logarithm laws
log(xy) = logx + logy log(x/y) = logx - logy log(x^b) = blogx log 1 = 0 lne = 1
