Find an equation of the plane that passes through the point (0,1,3) and is perpendicular to the planes 2x + y2z = 2 and x + 3z = 4.

1. Find an equation of the plane that passes through the point (0,1,3) and is perpendicular to the planes 2x + y−2z = 2 and x + 3z = 4. 

2.Find the velocity, acceleration and speed of a particle with the position function

r(t) = ti + t2j + 2k

at the time t = 1.

4. Find the limit or show that it does not exist (a) lim(x,y)→(0,0) xye^y x2+y2 (b) lim(x,y)→(0,0) xy √x2+y2

5. Find an equation of the tangent plane to the surface z = y2exy at the point (0,2,4)