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 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: 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: - 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: (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: 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: 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: 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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