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yopy
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I looked at the answer key and it said (1/3) (1,-2,1)
Does anyone know where the 1/3 came from?
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yopy said:i came up with doing the gradient of the ellipsoid. Then set that equal to the vector, <4,-4,6>. I solved and got x,y,z = 1,-2,1
Calculus 3, also known as Multivariable Calculus, is an advanced branch of mathematics that deals with functions of multiple variables. It is essential for understanding and solving real-world problems in fields such as physics, engineering, economics, and more.
Tangent planes and surfaces are concepts in Calculus 3 that involve finding the slope or rate of change of a function at a specific point on a curved surface. A tangent plane is a flat surface that touches a curved surface at a single point, while a tangent surface is the collection of all tangent planes at different points on a curved surface.
The equation of a tangent plane can be found by using the partial derivative of a function with respect to each variable at the point of tangency. These partial derivatives are then used to calculate the slope of the tangent plane, which is used in the equation of a plane formula: z = f(a,b) + fx(a,b)(x-a) + fy(a,b)(y-b).
Tangent planes and surfaces have many real-life applications, such as in engineering for designing curved structures, in physics for understanding the behavior of objects in motion, and in economics for analyzing supply and demand curves. They also play a crucial role in computer graphics and animation for creating realistic 3D images and simulations.
Some common techniques for solving problems involving tangent planes and surfaces include using partial derivatives, calculating directional derivatives, and finding the equation of a tangent plane. It is also helpful to understand the geometric interpretation of these concepts and how they relate to the graph of a function.