1. Find the first and second partial derivatives: A. z=f(x,y) = x2y3 - 4x2 + x2y-20 B. z=f(x,y) = x+ y - 4x2 + x2y-20 2. Find w w w x2 - 4x-z-5xw + 6xyz2 + wx - wz+4 = 0 Given the surface F(x,y) = 3x2 - y2 + z2 = 0 3. Find an equation of the plane tangent to the surface at the point (-1,2,1) a. Find the gradient VF(x,y) b. Find an equation of the plane...
6. Find an equation of the tangent plane to the surface z = 4x2-y2 +2y at (-1,2,4) = V20-下一77 at (2,1) 7. Find the linear approximation of f(z. y) and use it to approximte (1.95, 1.08). 8. Find the differential of the function
2. Given the paraboloid: z + x2 + y2 = 6. a) Find the symmetric equations of the normal line at the point (1, 2, 1). b) Find the equation of the tangent plane at the point (1, 2, 1). Simplify. c) Find the angle of inclination of the tangent plane to the xy-plane in degrees. Round to the tenths place.
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...
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
Please explain b! 2. Let z = f(x, y) = ln(4x2 + y2) (a) Use a linear approximation of the function z = f(x,y) at (0,1) to estimate f(0.1, 1.2) (b) Find a point P(a,b,c) on the graph of z = f(x, y) such that the tangent plane to the graph of z = f(x,y) at the point P is parallel to the plane 2x + 2y – 2=3
consider the curve described by the equation: 4x2 - 3xy + y2 = 14 at any given point on this curve, we have dy/dx = -8x + 3y / -3x + 2y your task is to find the points on the curve where the tangent line is parallel to the line y = x What is the y-coordinate of the leftmost point on the curve where the tangent line is parallel to the lone y=x
f(1,y) = x² + 4xy + y2 – 2.c + 2y +1. f(x,y) has a horizontal tangent 1. Find all points (a,b,c) where the graph z = plane (parallel to the xy-plane). 0 has a horizontal 2. Find all points (a,b) where the level curve f(x,y) tangent line (parallel to the z-axis).
11. Evaluate S. 'S*(1 + 3x2 + 2y?) dx dy. 12. Find the volume in the first octant of the solid bounded by the cylinder y2 + z2 = 4 and the plane x = 2y. Graph for Problem 12 13. Find the volume under the paraboloid z = 4 - x2 - y2 and above the xy-plane. N Consider the solid region bounded above by the sphere x + y + z = 8 and bounded below by the...
5 and 6 please 5) Given the surface f(x, y, z) = 0 or z = f(x,y), find the tangent plane at P. a) z2 – 2x2 – 2y2 = 12 @ P=(1,-1,4) b) f(x,y) = 2x - 3xy3 @ 12,-1) c) f(x,y) = sin(x) @ (3,5) 6) Find an equation of the tangent plane and the equation of the normal line to surface f(x..zb=0 @P x2 + y2 + z2 = 9 P = (2,2,1)