For a fixed A R, define the curve C in R2 by the equation y-2xy...
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For a fixed A € R, define the curve C₁ in R2 by the equation y²-2xy = x¹ +Ax + 4. You can view this family of curves on Desmos. Note this demo will not help you justify your answers below. (2a) Prove that if A #-6 and A # 6, then C₁ is a regular curve. You may use WolframAlpha to solve a 1-variable quartic equation. (2b) This family of curves can instead be viewed as the z-slices of the surface S in R³ defined by the equation y²-2xy = x¹+xz +4 Use the implicit function theorem to show that this equation defines a 2-dimensional regular surface (2c) The curves C, and C_6 are regular at each point except (-1,-1) and (1,1) respectively. These points where C6 and C_6 fail to be regular are called singularities. View this surface and family of curves on Math3d. (Google Chrome is the most stable browser for Math3D.) Informally explain how the shape of the surface appears to relate to the singularities of C6 and C_6. Your explanation must discuss both the surface and the curves. For a fixed A € R, define the curve C₁ in R2 by the equation y²-2xy = x¹ +Ax + 4. You can view this family of curves on Desmos. Note this demo will not help you justify your answers below. (2a) Prove that if A #-6 and A # 6, then C₁ is a regular curve. You may use WolframAlpha to solve a 1-variable quartic equation. (2b) This family of curves can instead be viewed as the z-slices of the surface S in R³ defined by the equation y²-2xy = x¹+xz +4 Use the implicit function theorem to show that this equation defines a 2-dimensional regular surface (2c) The curves C, and C_6 are regular at each point except (-1,-1) and (1,1) respectively. These points where C6 and C_6 fail to be regular are called singularities. View this surface and family of curves on Math3d. (Google Chrome is the most stable browser for Math3D.) Informally explain how the shape of the surface appears to relate to the singularities of C6 and C_6. Your explanation must discuss both the surface and the curves.
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a Given equation y 2 xy x Ax 4 On drawing the curve in desmos we will get following cu... View the full answer
Related Book For
Introduction to Algorithms
ISBN: 978-0262033848
3rd edition
Authors: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest
Posted Date:
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