Coordinate Geometry
Lines
specify a line through two points
line through (1,2) and (2,1)
specify a line by slope and intercept
line, slope=1/5, y-intercept=3
Planes
specify a plane through three points
plane through (0, 1, 0), (5, 6, 7), and (6, 7, 8)
Quadrants
identify the quadrant that contains a given point
What quadrant is (1,2) in?
is (-2, 2) in quadrant 4?
plot a conic section and identify its type
x^2 - 2 y^2 = 1
find a circle passing through three points
circle through (0,0), (1,0), (0,1)
compute properties of a parabola
parabola with focus (3,4) and vertex (-4,5)
compute the area bounded by two curves
compute the area between y=|x| and y=x^2-6
specify limits on a variable
area between y=sinc(x) and the x-axis from x=-4pi to 4pi
compute the arc length of a curve
arc length of y=x^2 from x=0 to 1
length of the curve {x=2cos(t), y=2sin(t), z=t} from 0 to 7
find the tangent to the graph of a function at a point
tangent to x e^-x^2 at x=1/3
find the normal to a curve specified by an equation
normal to 3x^2-2xy+y^2=1 at x=0, y=1
compute the curvature of a plane curve
curvature of sin(x)
compute the curvature of a space curve at a point
what is the curvature of (s, sin s, cos s) at s=2
locate stationary points of a function
stationary points of (x^5+x^9-x-1)^3
find stationary points of a function of several variables
stationary points (3x+1)y^3 + x^2 y
locate intercepts of a line or curve in the plane
y-intercept of 3x-4y=5
locate intercepts of a plane or surface
z-intercepts of x/2 - y/3 + z/12 = 2
locate inflection points of a function
inflection points of x+sin(x)
find inflection points in a specified domain
inflection points of e^sin(x^3) with -2<=x<=2
locate saddle points of a function
saddle points of x^3 - y^3 - 2xy + 6
find the saddle point nearest to a specified point
saddle point of sin(x y)-tan x near (5,6)
compute asymptotes of a function
asymptotes (2x^3 + 4x^2 - 9)/(3 - x^2)
asymptotes of erf(x)
find cusps on the graph of a function
cusps of sqrt |x-2| - cbrt |x+2|
find corners on the graph of a function