Please sketch the following (do it by hand and not software): a) The space curve defined by r(t) = t²j + (1 − t)k Where -1 ≤ t ≤1 b) The surface defined by x^2=y^2+z^2

Q: Assume S is the surface x1000 + y8000 + z1000 = 1,000,000 and F = [9 + ee^(xyz), x8yz, 3x - 5y -…

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Q: find the angles between the curves v=u2, v=u3, lying on the surface  x=u2+v2 y=u2-v2 z=uv+3u+2v

A: As per the question we are given the parametric form of a surface in 3d as : x = u2 +v2 y = u2 - v2…

Q: Find a point on the surface x+4y--z² =1 where the tangent plane is parallel to the plane x+4y- z =…

A: we need to find gradient of given surface to know about direction of normal vector to tangent plane

Q: For a given surface z-x^2-y^2=10 Find the parametric representation of the straight line which…

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Q: Sketch the following surfaces. 1) 4x^2+9z^2=9y^2 2)y^2-x^2=z Show all work.

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Q: Chow is it called, #8 Given the surface x²+ y² = Z² Sketch in 2D the level curve 4 corresponding to…

A: The surface x² + (y²/4)= (z²/9) is an elliptic paraboloid.The level curve for z=12 is an ellipse…

Q: A surface is defined by coordinate or parametric functions of more than two variables. Select one:…

A: A surface is defined by coordinate or parametric functions of more than two variables.

Q: - Graph the surface 1 = y² + z² — by first sketching at least three cross sections in each of the xy…

A: To Plot: Graph The Surface 1=y2+z2-x24 by plotting at least three cross section in xy and yz plane

Q: The horizontal tangent plane of the surface z = 4x – xy – 2y – 2x – 8y – 3 is given by the equation…

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Q: The surface z = x² - y² and the surface ryz = -30 intersect along a curve in R³. Find a vector…

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Q: (10) Let f(x, y) = /x-y a) Find the domain and range of f (x, y). Sketch the domain on the x-y…

A: Step:-1 Given that fx, y =x-y Part (a):- The square root function is real when x-y≥0 x-y≥0⇒x≥y⇒y≤x…

Q: Determine the surface area of the solid obtained by rotating the following parametric curve about…

A: Given: x=9+t2, y=2t, 0≤t≤2

Q: Find the lines curvatures, the first and second fundamental forms of the surface: the surface

A: As per the question we are given a surface. And we have to find its first and second fundamental…

Q: f(x,y)=9-x^2- y^2

A: We have to find standard form of the given equation and then identify the surface

Q: /Sketch the Surface Z=V9-X+y- and verify that fxg = Exx %31

A: Second order Partial Differentiation

Q: Which of the following is the coordinates of all points on the surface with equation z = x³-5xy¹…

A: To find the coordinates of all points on the surface where the surface has a horizontal plane, we…

Q: Describe and sketch the surface given by the function.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find equations for the a) tangent line and b) normal plane to the curve made by the intersection of…

A: Given The given surfaces are 3x2y+y2z=-2 and 2xz-x2y=3.  The given point is 1,-1,1.

Q: If z = f (x, y) is a smooth continuous surface such that f.(a,b) =0 and f,(a,b) =0 then what can you…

A: Please see the explanation below

Q: e'y x+y² a) Find the equation of the tangent plane to the surface at the point P(0, -2). Present…

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Q: Describe the surface whose equation is given by x² + y² + z² + 6y - 2z = 0.

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Q: y² - (z²/3) = 1 + (x²/12) sketch the quadric surface. emphasize the traces on the coordinate planes…

A: Given a quadric surface y2-z23=1+x212. YZ trace: When x=0, we get y2-z23=1. This is a hyperbola on…

Q: Suppose you head toward the xy-plane from the surface x? + y? – 2² = –1 at the point (1, 1, v3) by…

A: given,     x2+y2-z2=-1 at the point 1,1,3

Q: Find a parameterization for a circle of radius 4 with center (-4,4,-6) in a plane parallel to the yz…

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Q: Identify a generating curve on the rz-plane for the surface of revolution with equation 1² + y² + zª…

A: The equation of the surface of revolution given is as follows:…