Math 208 Final Exam Review Questions with
Verified Correct Answers
Distance in 2-space; given 2 pts (x,y) and (a,b)
sqrt((x-a)^2 + (y-b)^2)
Distance in 3-space; given 2 pts (x,y,z) and (a,b,c)
sqrt((x-a)^2 + (y-b)^2 + (z-c)^2)
characteristics of unit sphere
1=x^2 + y^2 + z^2; surface of sphere, center @ orgin, radius of one
shift function in the z direction up three, f(x,y) = x^2 + y^2
f(x,y) + 3
graph flip
-x^2 -y^2
shift circle eqn to have vertex of (0,1)
k(x,y) = x^2 + (y-1)^2
asymptotic
refers to when the graph flattens out. gets closer to the plane without ever touching it
cross section
view of a function when holding one variable fixed and allowing the others to vary
, equation of a plane given a point on the graph (x0,y0,z0), slope in the x direction, m, slope
in y direction, n
z = z0 + m(x-x0) + n(y-y0. Can replace z for f(x,y)
displacement vector of two points P(a,b,c) and Q(x,y,z)
magnitude and direction betwen two points : vecPQ = (x-a)i + (y-b)j + (z-c)k
magnitude of a vector <x,y,z>
sqrt(x^2 + y^2 + z^2)
Unit Vector Formula
v/||v||
how to find speed from a velocity vector
magnitude of the vector
geometric definition of dot product v*w
||v|| ||w|| cos(theta); where theta is equal to the angle between the two vectors
algebraic definition of dot product v*w
v1w1 + v2w2 + v3*w3
equation of a plane given normal vector, n = <a,b,c>, and a point P = (x0,y0,z0)
a(x-x0)+ b(y-y0) + c(z-z0) = 0
what is the same as the coefficients of the normal vector
the equation of the plane is the same as the coefficients of the normal vector
Verified Correct Answers
Distance in 2-space; given 2 pts (x,y) and (a,b)
sqrt((x-a)^2 + (y-b)^2)
Distance in 3-space; given 2 pts (x,y,z) and (a,b,c)
sqrt((x-a)^2 + (y-b)^2 + (z-c)^2)
characteristics of unit sphere
1=x^2 + y^2 + z^2; surface of sphere, center @ orgin, radius of one
shift function in the z direction up three, f(x,y) = x^2 + y^2
f(x,y) + 3
graph flip
-x^2 -y^2
shift circle eqn to have vertex of (0,1)
k(x,y) = x^2 + (y-1)^2
asymptotic
refers to when the graph flattens out. gets closer to the plane without ever touching it
cross section
view of a function when holding one variable fixed and allowing the others to vary
, equation of a plane given a point on the graph (x0,y0,z0), slope in the x direction, m, slope
in y direction, n
z = z0 + m(x-x0) + n(y-y0. Can replace z for f(x,y)
displacement vector of two points P(a,b,c) and Q(x,y,z)
magnitude and direction betwen two points : vecPQ = (x-a)i + (y-b)j + (z-c)k
magnitude of a vector <x,y,z>
sqrt(x^2 + y^2 + z^2)
Unit Vector Formula
v/||v||
how to find speed from a velocity vector
magnitude of the vector
geometric definition of dot product v*w
||v|| ||w|| cos(theta); where theta is equal to the angle between the two vectors
algebraic definition of dot product v*w
v1w1 + v2w2 + v3*w3
equation of a plane given normal vector, n = <a,b,c>, and a point P = (x0,y0,z0)
a(x-x0)+ b(y-y0) + c(z-z0) = 0
what is the same as the coefficients of the normal vector
the equation of the plane is the same as the coefficients of the normal vector
