Find an equation of the tangent plane to x2+y2+z2=34 at the point (3,4,3).
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Find an equation of the tangent plane to x2+y2+z2=34 at the point (3,4,3).
Find the point(s) on the sphere x2 + y2 + z2 = 1 where the tangent plane is parallel to the plane 2.C + V3y – 3z = 2. Then write the equation(s) of the tangent plane(s). (Explain how you found the point(s) and simplify the equation(s) of the tangent plane(s)).
7) Consider the surface S: x2 +y2 - z2 = 25 a) Find the equations of the tangent plane and the normal line to s at the point P(5,5,5) Write the plane equation of the plane in the form ax + By + y2 + 8 = 0 and give both the parametric equation and the symmetric equation of the normal line. b) Is there another point on the surface S where the tangent plane is parallel to the tangent...
5. Find the equation of the tangent plane to z = x2 + y2 at (x, y) = (1,2). 6. Set up (do not evaluate) iterated integrals for both orders of integration of ydA, where D is the region bounded by y = x2 and y = 3x.
Find the equation of the tangent plane to the surface at the given point a. z = x2 + y2 + 2 (1,3,12)
Find the equation of the plane tangent to the following surface at the given points. x2 + y2 - 2? + 5 = 0; (4,2,5) and (-2,-4,5) The equation of the tangent plane at (4,2,5) is = 0. the equation of the tangent plane to the surface
Find a normal vector and an equation for the tangent plane to the surface: x3 - y2 - z2 - 2xyz + 6 =0 at the point P : (−2, 1, 3). Determine the equation of the line formed by the intersection of this plane with the plane x = 0. [10 marks] (b) Find the directional derivative of the function F(x, y, z) = 2x /zy2 , at the point P : (1, −1, −2) in the direction of...
Partial derivatives Example Find the equation of the tangent plane and the normal line at the point (1,1,1) to the surface 2x2 + 2y2 + 3z2 = 6. Example Find the equation of the tangent plane and the normal line at the point (1, 2, 3) to the surface 2x2 + y2 – z2 = -3.
(a) Find and identify the traces of the quadric surface x2 + y2 ? z2 = 25 given the plane. x = k Find the trace. Identify the trace. y=k Find the trace. Identify the trace. z=k Find the trace Identify the trace. (b) If we change the equation in part (a) to x2 ? y2 + z2 = 25, how is the graph affected? (c) What if we change the equation in part (a) to x2 + y2 +...
6. Find the equation of the tangent line at the given point. (a) x2 + y2 = 25,(-3, 4) (b) 2y - Vt = 4,(16, 2) (c) y + xy² + 1 = x + 2yº, x = 2
Find the equation of the tangent plane to the surface 2x2 + y2 + 2z2 = 5ey + 5 at the point (1,0,2).