Homework SourseFind the equations of the following A xz4 arctanyz 1pi11 B t
Find the equations of the following.
A)
x-z=4 arctan(yz), (1+pi,1,1)
B) the normal line to the given surface at the specified point. (enter your answer in terms of t)
x=1+pi+t
y=?
z=?
A)
x-z=4 arctan(yz), (1+pi,1,1)
B) the normal line to the given surface at the specified point. (enter your answer in terms of t)
x=1+pi+t
y=?
z=?
Solution
Answers: 4arctan(yz) + z - x = 0 Find the gradient: dF/dx = -1 dF/dy = 4z/(1 + y^2*z^2) dF/dz = 4y/(1 + y^2*z^2) + 1 Find the gradient at the point given: dF/dx = -1 dF/dy = 4/2 => 2 dF/dz = 4/2 + 1 => 3 -1(x - (1+pi)) + 2(y - 1) + 3(z - 1) = 0 (-x + 1 - pi) + 2y - 2 + 3z - 3 = 0 3z= 4 + pi + x - 2y z = (x - 2y + 4 + pi)/3 A)tangent plane: 1-2y-3z=-4+pi B) y = 1-2t , z = 1 - 3t
