Find an equation of the plane tangent to the following surface at the given point. 7xy+yz+4xz-48=0;\ (2,2,2)

Find the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1).

Evaluate the double integral ${\displaystyle y^{2}dA}$, D is the triangular region with vertices (0, 1), (1,2), (4,1)

Parametric to polar equations Find an equation of the following curve in polar coordinates and describe the curve. $x=(1+cost)cost,y=(1+cost)sint,0\le t\le 2\pi$

Using the point ${\displaystyle P_0=(1,0,-2)}$ and the vector $v=(1,3,-1)$ write a parametric vector equation for a line through ${\displaystyle P_0}$ in the direction of v

Curves to parametric equations Find parametric equations for the following curves. Include an interval for the parameter values. Answers are not unique. The line segment starting at $P(-1,-3)\text{and ending at}Q(6,-16)$

Graph the sets of points whose polar coordinates satisfy the equations and inequalities ${\displaystyle r\ge 1}$

Let C be the curve described by the parametric equations x(t)= t, y(t) =${\displaystyle t^3}$
a) sketch a graph of C
b) find the vector-valued function f(t) associated with this parameterization of the curve C.