Q: A natural cubic spline S on (0,2] is defined by Jsin - 1+2-r. S) = if Osr<l. |S,0) = 2+ b - 1) + cư…
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Q: Use Green Theorem to evaluate C P xydx+e'dy where Cis the path from (0,0) to (1,1) along the graph…
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Q: For z € C, define Tz: CC by Tz(u) = zu. Characterize those z for which Tz is normal, self-adjoint,…
A: Given that: For z∈C, Define Tz:C→C by Tzu=zu. The objective is to verify the given statement. Now…
Q: 3. Compute the inner product g (v,w) of v = + x. 2 əx and w = x.-+ 2y. Əx ay' Where the line element…
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Q: If W(-10, 4), X(-3, -1), and Y(-5, 11) dassify AWXY by its sides. Show all work to justify your…
A: Given, If W-10, 4, X-3, -1, and Y-5, 11 of ∆WXY.
Q: Find the image of the semi-infinite strip x ≥ 0, 0 ≤ y ≤ π under the transformation w = exp z, and…
A: w lies in the portion of the closed upper half-plane external to the open unit disk.
Q: Given that C = C₁ U C₂ U C3, where C₁ is the line segment from (−1, −1) to (0, 0), C₂ is the line…
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Q: 28. Show that the circulation of F(x, y, z) = (x², y², z(x² + y²)) around any curve C on the surface…
A: Given figure Stoke's Theorem Here take single integral over closed path C and double integral over…
Q: 7. Use Green's Theorem to evaluate the integral f x²y dx - xy²dy where C: is the circle x² + y² = 4…
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Q: Let o be the hypercube [0, 1]". For any f e C[0, 1] show that (). (x1 + x2 + + Xn dxjdx2 dxn = f ...…
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Q: Let M be an elliptic paraboloid z = y² + 2?. (A) "Compute the Gauss map and the shape operator. (B)…
A: Answer for sub question a: Given x=y2+z2 A parametrization is given by: Xu,v=u2+v2,u,v Then,…
Q: Let A = = اه هب را ره and ve lation R, R2R3 and Ry on A, what Would graph be their directed ام مه…
A: R1=a,a,c,c,b,b,d,d The directed graph is:
Q: Prove that the circle {(x, y), x² + y² = 1} is hot homeomorphic to the interval [-1, 1].
A: We will prove this result by contradiction: Suppose there exists a homeomorphism between -1,1 and S…
Q: Show that the following subsets of C[0, 1] are isometric: X {fe C[0, 1]: f(1/2) >0} {fe C[0, 1]:…
A: Given : X=f∈C0 , 1 : f12>0Y=f∈C0 , 1 : f12<0 Show that : C0 , 1 and C0 , 2 are…
Q: 1)Prove that the curves o, = {|z|=2} y 0, = {|z- i|=4} are homotypic. 2)calculate O z*dz and o z*dz…
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Q: Calculate the circulation of A = p cos ap + z sin o az around the edge L of the wedge defined by 0 ≤…
A: Yes , we can solve using stokes theorem. Note that all the cases z = 0
Q: Let X,Y,T be dotined poinds. Show that if Te X Ÿ then XY = %3D
A: It is given that on considering that let X,Y,T be the distinct points The objective is to show that…
Q: Let M be an elliptic paraboloid a = y? + z². Compute the Gauss map and the shape operator. Find k…
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Q: 39. Show that the graph of r =t sin ti + t cos tj + t'k lies on the paraboloid z = x² + y².
A: Here we compare r as its basic equation to prove this.
Q: 23 + 3 4. Evaluate the integral dz, where C is the circle (a) |z + 3| = 3, (b) |z| = 3, (c) |z| = 7.…
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Q: Use Greens Theorem to evaluate: §. (2x + ev´)dy - (4y2 + e*")dx where C is the boundary of the…
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Q: show that the. fallowing Complex functron is dis continuous at z=? 121 1 fCZ) = スー! %3D 3. %3D
A: Topic:- limit and continuity
Q: tnd the kes reetor projection of anto r if
A: Given : u→=5i→+2j→ and v→=6i→-3j→
Q: Let F(x, y, z)=z²i+ 2xj+y°k and let S be the graph of z = 4-x² -y², z 20 oriented counterclockwise.…
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Q: Given that C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, -1) to (0, 0), C₂ is the line…
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Q: bound the module of the contour integral (image) where C= { z E C : |z - 1| = 2}}
A: Introduction: Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement…
Q: For z ∈C, define Tz: C →C by Tz(u) = zu. Characterize those z for which Tz is normal, self-adjoint,…
A: Firstly, find out Tz*.
Q: Show that [0, o0) and [1, o0) are isometric.
A: We need to show that , [0 , ∞) and [1 , ∞) are isometric. We know that two metric spaces X and Y…
Q: 4 Let y = U2 = -7 U1 = -4 4 -6 -2 -9 Compute the distance d from y to the plane in IR° spanned by u̟…
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Q: Given that C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C₂ is the line…
A: This is a problem on Green's Theorem. The problem has been solved step by step. See the solution.
Q: , a curve in the z-plane and a complex mapping w = f(z) are given. In each case, find the image…
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Q: 5. Find the curl of U = e*yax + sin(xy) a, + cos² (xz) az. A. 2z cos(xz) sin(xz) a, + [x cos(xy) –…
A: FORMULA USED- For f¯=pax+qay+razcurl f=axayaz∂∂x∂∂y∂∂zpqr
Q: 2. 22 – x2 1 By sketching the traces on the ry-, rz- and yz-plane a.
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Q: Given that C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, -1) to (0, 0), C₂ is the line…
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Q: Consider the surface: S:z = 4 – a?, in the first octant and bounded by x² +y°, as shown in the…
A: The equation of the surface given is as follows: z=4-x2 The surface is bounded by the curve x2+y2=4.…
Q: Consider the solid generated by the surfaces octant the 1st in
A: The surfaces are given by x2+y2+z2=4 and y2+z2=2 To find the volume bounded by two surfaces in the…
Q: which of the sets is orthvoonal under the given inner product on C[0, 1] ? = S furgex) dx I. {1,…
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Q: If the Wronskian of f and g is t cos t - sin t, and if u = f+ 2g, v = f - g, find the Wronskian of u…
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Q: Let R be the region in the first quadrant bounded by x = = 1, (x − 2)² + y² = 1, and x² + y² = 4.…
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Q: Complex Analysis
A: For given function, First we will show the function is harmonic function as shown below :From the…
Q: Consider the 2nd order PDE -3u +6xu-3u w=cos(x). XX ху yy (a Determine the regions in the xy-plane…
A: Consider the PDE: -3uxx+6xuxy-3uyy=cosx. A second order PDE of the form…
Q: Let D be the solid region in the first octant bonded above by z-3 and below by 2= 2++y. Then the…
A: Here we will have to project the 3-dimensional solid regions on a 2-dimensional plane. Hence, we…
Q: The curl of f(x,y,z)=xyzj is None of these. хуk-yzi О ху-yzk ООО О
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Q: Evaluate |(y zi+y°i+xzk)•d$ where S is the boundary of a cuboid defined by S -15x<1, -1<ys1 and…
A: The given integral: S=∬s(y2zi→+y3j→+xzk→) dS Where S is the boundary of cuboid defined by -1≤x≤1,…
Q: 1. Use a change of variables to evaluate [[ y- dA where R is the trapezoid with vertices (1,0,…
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Q: Use Green's Theorem to evaluate S. axy dy + cxy dy, where C is a counterclockwise oriented…
A: Given : a=2, c=8 We have to use Green's Theorem to evaluate ∫C axy dy+cxy dy where C is a…
Q: Let F: IR3 →IR3 is a diffeomorphism and M is a surface in IR3 , prove that the image F(M) is also a…
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Q: Given that C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, -1) to (0, 0), C₂ is the line…
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- Apply the transformation T (x, y) = (0.8x − 0.6y, 0.6x + 0.8y) to the scalene triangle whose vertices are (0, 0), (5, 0), and (0, 10). What kind of isometry does T seem to be? Be as specific as you can, and provide numerical evidence for your conclusion.For z ∈C, define Tz: C →C by Tz(u) = zu. Characterize those z for which Tz is normal, self-adjoint, or unitary.this question is differential geometry Let F: IR3 →IR3 is a diffeomorphism and M is a surface in IR3 , prove that the image F(M) is also a surface in IR3.
- Find the moving trihedral of C for all t ∈ (0, π). [ THIS IS NOT A GRADED QUESTION ]For G:R^2 to R^2 defined by G(x,y)=(x^3+y,y+2x) , show that G is an immersion and a topological embedding.Show that D^2 = {(x, y) ∈ E^2: x^2+y^2 ≤ 1} ⊂ E^2 and the space containing a single point are homotopy equivalent. (E^2 represents R^2 equipped with euclidean topology)
- Find the image of the semi-infinite strip x ≥ 0, 0 ≤ y ≤ π under the transformation w = exp z, and label corresponding portions of the boundaries.Prove that the reflection along the line y = −x is equivalent to reflection along the y-axis followed by a counter-clockwise rotation by 90◦ .Figure ABCD maps to WXYZ with the following transformations: (x,y)→(x−3,y+4)→(4x,4y)→(−x,−y)(x,y)→(x−3,y+4)→(4x,4y)→(−x,−y) If WX=8, what is the length of AB
- Let X=(x1,x2) and Y==(y1,y2) belongs to R^2. Verify that<X, Y> = 5(5x2y2+ x1y1-2x1y2-2x2y1) is an inner product on R^2Suppose S is the unit cube in the first octant of uvw-space withone vertex at the origin. What is the image of the transformationT: x = u/2, y = v/2, z = w/2?In the frieze group F7, show that yz = zy and xy = yx.