Can someone help me with this problem? I'm trying to find the equation of the line tangent to the intersection of the surface z = arctan(xy) with the plane x = 2 at the point (2, 1/2, pi/4).
Since x is held constant we are finding the partial derivative wrt to y, i.e.
d(arctan(xy))/dy = 1/(1+(xy)^2) * x = x/(1+(xy)^2) where d/dy is a partial derivative. The slope of the line is given by the value of (partials) dz/dy at (2,1/2) which is precisely 1. I know now that the parametric equations will be given by:
x = 2
y = 1/2+ ?
z = pi/4 + ?
Can somebody explain to me how to get the terms containing t in the parameterizations for y(t) and z(t)? I would really appreciate it.