Let (X,d)be full m.J,P, defined as D:Xx X R,plxy=min{1, d , is the full metric on X, show. (functional analysis )'
Q: 1. Prove that fo r*dr + rydy = where C1 is the line segment from (0,0) to (1,0) by using…
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Q: find the tangent plane to the surface z = Vy-x at the point (1,2,1)
A: Equation of tangent plane is z-c = df/dx(x-a)+df/dy(y-b) at point (a,b,c)
Q: 2. Prove that fo r*dr + xydy = -+- where C2 is the line segment from (1,0) to (0, 1) by using…
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Q: Does the Divergence Theorem apply to surfaces that are not closed?
A: By Stokes' theorem:
Q: Let L denote the intersection line between the planes 2x-y-3z=4 and 2x+y-z=2 A) Determine a…
A: Solution of the system of equation will give the equation of the line of intersection.
Q: Find the tangent plane (Xo, Yo, Zo) from f (x, y) = x² - 3y²; (0,1, -3)
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Q: Find the ar ea of sur face x - 2y - 2z = 0 that lies above the triangle bounded by the lines x = 2,…
A: Given : The surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x…
Q: Compute the distance d from y to the plane in R' spanned by u1 and uz.
A: We have to find the distance d from y to the plane in R^3.
Q: Find a unit vector normal to the surface x^3- xyz + z^3 = 1 , at the point (1, 1, 1)
A: To find the unit normal vector to the surface x3-xyz+z3=1 at the point 1, 1, 1
Q: What is the value of F.ds, where F = 4xz,- y° i, + yz, ? Here, s is the surface bounded by x = 0, x…
A: Here function is given find f.ds as below
Q: Let C denote the circle of radius 1 in R2 centered at the origin, oriented counterclockwise. for…
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Q: Write a homeomorphism between the unit closed disk A = {(r,y E R2 : a2 + y? < 1)} and the unit…
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Q: Use Divergence Theorem to evaluate ,0²z²i + z²x²j+ x²y²k).ds, 1. where S is the upper part of the…
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Q: S how that the line af intesection of the Planes and 5x-2y-Z=0 X+2y-22= 5 is Paralkel to thelime メ+3…
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Q: 21. r(t) = t³ j + t² k %3D
A: Given r(t)=t3j+t2k
Q: A _____ is the set of points (x, y) in a plane such that the difference in distances between (x, y)…
A: The standard form of the equation of the hyperbola is,
Q: A normal vector to the tangent plane for the surface z = , at the point (1, 1, 1) is: y - Select…
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Q: Determine the curvature of the graph of y = In x at the point where x = 1.
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Q: Let the the position vecor be R(t) = (-t,2 cos(2t),2 sin(2t)). Compute the curvature x(t).
A: The position vector Rt=-t,2cos2t,2sin2t. We have curvature k(t).
Q: Find vohume fome above ZVy-xLy, below Z0(xy plane) inside xy/ 3.
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Q: = xyi + yzĵ + de is a in x-y plane.
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Q: Find the equation for the tangent plane to the surface z= 7x2. 10y² at the point (2, 1, 18). O 2x +…
A: Equation for the tangent plane to the surface z=f(x, y) at the point (a, b, f(a, b)) is given by
Q: Use Theorem 11.24 to prove that the curvature of a linearfunction y = mx + b is zero for every value…
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Q: Suppose that the plane tangent to z = f(x,y) at (-2,3,4) has equation 4x + 2y + z = 2. Estimate…
A: As the given plane tangent to z=f(x,y) at (-2,3,4) is 4x+2y+z=2, that is z=2-4x-2y thus the…
Q: 4) Find the families of lines of curvature of the surface z = r + y? .
A: Given: z=x2+y2
Q: z = tan (VZn + Ze
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Q: Assume S is a smooth surface parametrized by R(u,v) = (V / za sin y do. Evaluate S Hint: Find the…
A: We use double integral to solve this.
Q: Show thata perojective plane of gives 0nder indeed BİBD (+n+l, n+),1)
A: We need to show that the projective plane of order n indeed gives a BIBD (n2+n+1,n+1,1)
Q: Use Stoker Cur theorem to evaluate. IF - ds S Where F= of radius I with x ] +ya³k ands is the +yx³k…
A: Given That ∬Curl F →·dS→ F→=yi-xj+yx3k To Find: evaluate ∬Curl F →·dS→ using strokes theorem
Q: Calculate both sides of Green's Theorem when F = [-x²y, xy²] and y positively oriented circle x2 +…
A: According to the given information it is required to calculate both sides of the Green’s theorem.…
Q: The plane tangent to the surface z+1= ze" cos z at (1,0,0) can be represented by the equation Z= 1.…
A: As per our guidelines, we are allowed to answer only one question. Since you have posted multiple…
Q: Let C be the line segment from point (0, 1, 1) to point (2, 2, 3). Evaluate line integral yds. C
A: To evaluate the line integral
Q: Find the equation of the tangent plane to the surface z = In (2x + y) at the point (-1, 3, 0) . O x…
A: The equation of the tangent plane to the surface Z=fx,y atthe point a,b,fa,b is given by…
Q: Please do no 3 for me using definition of Metric spaces
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Q: find the curvature of y=x^4 at (1,1).
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Q: The normal vector to the tangent plane for the surface xy² z³ 2 3 = -4, at the point (1, 2, -1) is:…
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Q: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y
A: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y
Q: Compute the orthogonal projection of point A coordinates (2,0) onto the Set M (the closed unit disk…
A: I have given the answer in the next step. Hope you understand that
Q: The plane tangent to the surface z +1= re" cos z at (1,0,0) can be represented by the equation X + y…
A: Given: z+1=xey cosz
Q: Let C be a curve given by the intersection of the surfaces z = x2 +y2;z = 3−2x . The value of the…
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Q: Let r (t,t,t) be a curve in 3-dimensional space having unit tangent and norma V2 vectors u and n.…
A: We will use formula of curvature of a curve to solve it.
Q: Does the the paraboloid z = 1 – 2x² - - y² have a tangent plane at some – x + y + z = 1?
A: Introduction: Let P0=(x0,y0) is a point in the domain of f, and S is a surface defined by a…
Q: Verify Divergence theorem for the function F = e,p over the semi-cylindrical volume { x* +y° sa…
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Q: Let 3 : (3t, r = be a curve in 3-dimensional space having unit tangent and normal vectors u and .…
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Q: Let C be the positively oriented circle x² + y² = 1. Use Green's Theorem to evaluate the line…
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Q: Show that the Gauas and mean curvatures on , X = (u + v,u –- v,uv) at u = 1, v = 1 are K = 116 and H…
A: Given, X=u+v,u-v,uv u=1,v=1 , k=116 and H=182 We know that, E=xu,xuF=xu,xvG=xv,xv So, we need to…
Q: x= 0, x= π &x= π
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Q: (2) Let S be the surface of the sphere of radius 4 centered at the origin oriented away from the…
A: We can apply divergence theorem to find this
Q: Evaluate the line integral 3xy ds where Cis line Segment Joining (-5,7) to (3,1) the
A: Introduction: A line integral in calculus is an integral where the function being integrated is…
Q: Evaluate | xyzdx + In(xy)dy + xzdz over the straight line segment from (2, 1, 1) to (–1,1, –2)
A: We need to evaluate integral∫Cxyzdx+lnxydy+xzdz over the line segment from 2,1,1 to -1,1,-2.
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- Could you also please show work for the velocity find the velocity using calculus?ry. The directional derivative of f )in the directional (6, 2 and at the point (2, y) - (6,- 4) is Question Help: OVideo Submit QuestionWhat is special about the derivatives of vector functions of con-stant length? Give an example.
- Consider the velocity functionfor an object moving along a line as showna. Describe the motion of the object over the interval [0, 6].Show that the curve F(e) = lies in a plane.Let (a, b) be an arbitrary point on the graph of y = 1/x, x > 0. Prove that the area of the triangle formed by the tangent line through (a, b) and the coordinate axes is 2.
- Find the equation of the plane tangent to the graph of f at the point (2,0,2)What is the definition of the directional derivative for afunction of three variables, f (x, y, z)? Be sure to includethe words “unit vector” in your definition.Sorry about 3b question, if the tangent line become (2,0) b. Calculate its tangent line at (2,0) in the projective plane and verify the result by comparing it to its Euclidean representation! What will be the different?
- Find and equation of the tangent planeFind the equation of the tangent line to the curve of intersection of the surface z = x² - y² with the plane x = 9 at the point (9, 1,80). (Express numbers in exact form. Use symbolic notation and fractions where needed.) equation:Derive the relation A,(to) = 47 S, (r)², as given in Equation 6.24, starting from the Robertson-Walker metric of Equation 6.22. 6.7 ds? = -c²dr² + a(t)°[dr² + S« (r)²d$²), (6.22) Ap(to) = 4x S, (r)². (6.24)