Taylor Series, Maclaurin Series, Conic Sections

taylor series basics

taylor series formula

• derived from power series formula and derivs of the power series

maclaurin series formula

• a subgenre of the taylor series

taylor/maclaurin polynomial

a polynomial of degree n

• basically just the series

distance formula for 3D coord sys

equation of a sphere

• the eqn is special if the center coord is (0,0,0)

conic sections: eclipse (basic concept)

conic sections: eclipse defn

• major axis → the line w the foci pts

conic sections: the components of an eclipse

conic sections: labelled diagram of an eclipse

conic sections: analysis of a diagram of an eclipse

conic sections: formulas for eclipse

** see the diagram of eclipse in notes

center = (h,k)

vertices = (h-a, k) and (h+a, k)

foci = (h-c, k) and (h+c, k)

parabola

a set of pts in a plane that are equidistant from a fixed pt F (focus) and a fixed line called the directrix

• the defining property of a parabola is that every pt that makes up the parabola meets the following requirement:

  • the dist b/w the pt and the focus = the dist b/w the pt and the directrix

parabola formulas

hyperbole defn

hyperbole formulas