(a) Find an equation of the tangent plane to the surface at the given point. x + y + z = 14, (5, 5, 4) (b) Find a set of symmetric equations for the normal line to the surface at the given point.
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- (a) Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 14, (1, 3, 2) (b) Find a set of symmetric equations for the normal line to the surface at the given point.Find an equation of the tangent plane to the surface at the given point. X²+y²+z²=14, (1,2,3) And find a set of symmetric equation for the normal line to the surface at the given point. ○X-1/1 = y-2/2 = z-3/3 ○X-1/14 = y-2/14 = z-3/14 ○X/1 = y/2 = z/3 ○X/14 = y/14 = z/14 ○X-1 = y-2 = z-3This is a two-part problem. I. Find the equation of the tangent plane to the surface x = 4y^2 + 3z^2 - 465 at the point (10, -10, -5). Make the coefficient of x equal to 1. II. Find the equation of the normal line to the surface x = 4y^2 + 3z^2 - 465 at the point (10, -10, -5). Make the coefficient of x equal to 1.
- Find parametric equations for the normal line to the surface z=-7x2 -9y2 at the point (2,1,-37)Find an equation of the tangent plane to the surface x2 + y2 + z2 = 9 at the given point (1, 2, 2) and find a set of symmetric equations for the normal line to the surface at the given point.Find an equation of a generating curve given the equation of its surface of revolution. x2 + y2 − 2z = 0
- find parametric equations for the line tangent to the curve of intersection of the surfaces at the given point. 1. Surfaces: x + y2 + z = 2, y = 1 Point: (1/2, 1, 1/2) 2. Surfaces: x3 + 3x2y2 + y3 + 4xy - z2 = 0, x2 + y2 + z2 = 11 (1, 1, 3) Point: 3. Surfaces: x2 + y2 = 4, x2 + y2 - z = 0 Point: (sqrt(2), sqrt(2), 4)Find an equation of the tangent plane to the surface z = 16 − x2 − y2 at the given point (2, 2, 8) and find a set of symmetric equations for the normal line to the surface at the given point.A-) Find the equation of tangent plane to the surface x^2 + 2y^2 + 3z^2 = 21 which is parallel to the plane 2x + 4y + 6z = 3. B-)Find the extremum and saddle points of the function f (x, y) = x^3 − 3xy + y^3 if any.
- 1. (a) Write down an equation for the plane tangent to the surface √ x + √y + √ z = √ c at the point (x0, y0, z0). Assume c > 0 is a constant. (b) Show the sum of the x-, y- and z- intercepts of any tangent plane to this surface is a constant (that is, the same constant, no matter which tangent plane you’ve chosen!), and find the constant.Find an equation of the tangent plane to the surface y ln xz2 = 2, at the given point (e, 2, 1) and find a set of symmetric equations for the normal line to the surface at the given point.The slope of the surface z = xy² in the x-direction at the point (2, 3) is _____, and the slope of this surface in the ydirection at the point (2, 3) is _____