Vectored Valued Functions
What is the domain of:
r(t)=<2t,4t^2,1/(3-t)>
{t|t!=3}
find r'(t)
given
r(t)=<-2t^2-5,3e^(-4t),4sin(-2t)>
r'(t)=<-4t,-12e^(-4t),-8cos(-2t)
Find the point of intersection
u(t)=<4t,-3t>
v(t)=<t,-t>
<0,0>
u(t)=<2tsin(t),5cos(t),t+3>
v(t)=<5sin(t),2tcos(t),t^2-4>
findu(t)*v(t)
t^3+3t^2+6t-12
find r'(t)
given
r(t)=<2e^(5t),-2ln(3t),2t>
r'(t)=<10e^(5t),-2/t,2>
Find a vector parallel to:
x(t)=4-5t
y(t)=3+4t
z(t)=9t
r(t)=<-5,4,9>
Find a vector equation that represents the curve of intersection between
x^2+y^2=9
x=xe^y
r(t)=<3cos(t),3sin(t),3cos(t)e^(3sin(t))>
Find the integral of
r(t)=<cos(t),sin(t),3t>
<sin(t),-cos(t),3/2t^2>
Find the point at which the line intersects the yz plane
r(t)=<6-8t,-3-6t,-2-2t>
p=(0,-15/2,-1/2)
Find a vector equation that represents the curve of intersection between
z=4x^2+y^2
x=y^2
r(t)=<t,t^2,4t^2+t^4>
find the integral of
r(t)=<5t^2+4,1/t,4>
<5/3t^3+4t,ln(t),4t>
Find the equation of the plane with points
(7,3,1),(-4,4,-2),(1,3,5)
6(x-1)+12(y-3)+6(z-5)=0
Evaluate the limit of the function as t->0
r(t)=<2e^t,sin(t)/(-2t),(t-2)^2>
<2,-1/2,4>
Given
r(t)=<5t^2+1,-e^(-3t),2sin(-3t)>
Find the unit tangent vector at point t=0
1/sqrt45<0,3,6>
Find the equation of a plane through point (3,-6,-7)
and is orthogonal to the line
r(t)=<2+3t,1+4t,7-8t>
3(x-3)+4(y+6)-8(z+7)
or
3x+4y-8z=41