Evaluate aned on c indicatid curve 2. 2. y+ Y( sm3x +ca 32,22 3t ,4=t,0zt2|

Q: 3) Consider the curve C in R³ given by: r(t) = (t + In t, t – In t, 4t'/²) con 1<t< 2 An expression…

A: Formula: If r(t)=x(t), y(t), z(t), a≤t≤b is parametrization of a curve C then the line integral…

Q: Use Green Theorem to evaluate xydx+e\dy where Cis the path from (0,0) to (1,1) along thegraph of y…

A: Consider the provided question,

Q: 1. Use the Stoke's Theorem to evaluate y'dx + xy dy + xz dz, C where C is the bounding curve of the…

A:

Q: compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path…

A: compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path…

Q: Let C be a smooth curve traced by Ř(t) with R(1) = (2, –1, 1) and R' (1) = (1, –2, –1). Let g(t)…

A:

Q: 6. Set up but do NOT evaluate Evaluate the line integral 2 curve (t) - (t", t), where 0sts0. L ds,…

A: Consider the given integral as ∫Cyxds, where C is the curve r⇀t=t4,t3 and 0≤t≤1. Note that, the line…

Q: Suppose the closed curve C in R? starts at the point (-1,1), goes along the parabola y = x2 to the…

A:

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: Let C be a portion of a curve from (2,0) to (2,2). Let F(r,y) = (tan(x²) + e²v¸ 2re²v

A: Introduction: A vector field is conservative if ∂P∂y=∂Q∂x, Where f(x,y)=Pi+Qj.

Q: 10. Evaluate the integral cz(z-1) where C is a simple closed curve in the positive direction that…

A:

Q: Use Green's theorem to evaluate S. (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

A:

Q: 3.use Greens theorem S(1+x dx + 2xy dy ,where C is triangle With vertices (0,0),(1,0).(1,3) oriented…

A: "Since, you have asked multiple questions, we'll solve the first question for you. If you want any…

Q: 7. Given the space curve er(t) = (4 sin t ,4 cos t , 10t), Find T, N, B, and t (torsion)

A:

Q: 30. (2x + y²) dx + (2xy + 3y) dy C C: Any simple closed curve in the plane for which Green's Theo-…

A: We know that Green's theorem

Q: Let Y1, Y2,..., Yn N(µ, 4), where is the unknown parameter. Find the MVUE for µ².

A: Fisher-Neyman factorization theorem: Suppose X1, X2, …, Xn is a random sample of size n taken from a…

Q: 15. What is the correct piecewise parametrization of a path C created by starting from C₁ of…

A: Introduction: The parametrization is a very significant part that is related to vector calculus.…

Q: The dispiacement tunchon of Object A is S,(t) =t 3-2t²+4; and the cispiacement funchon of Object Bis…

A:

Q: 11. What is the symmetric equation of the normal line to the ellipsoid x? + 2y? + 32 = 6 at P(1,1,…

A: solution:  Given  ellipsoid⇒x2+2y2+3z2=6at point(1,1,1)let f(x,y,z)=x2+2y2+3z2-6

Q: Consider the cune C: (x-8)+ 4-7) When parametneing C, A tungent veotoar is i O a) r (0) = (8 +3…

A:

Q: Compute I = (2x²132²y+ 4xy)ax +(x'+2x²-y') dy+zdz along The curve C C4U Cz UG given in the figure…

A: Given To compute I=∫C2x3+3x2y+4xy.dx+x3+2x2-y2dy+zdz along the curve C=C1∪C2∪C3 given in the figure.

Q: (4,7, – 5) Evaluate the integral y dx + x dy + 8 dz by finding parametric equations for the line…

A:

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…

A:

Q: Exercise 1.3.2 Give a paramatrization for the curve curve y = x³ + ()x-¹, then deduce the length of…

A: Given curve is  y=16x3+12x-1

Q: Let C be the curve in space given by the following parameterization. r(t) = tỉ + t²j + 9k, 0 < t s…

A:

Q: 4. Prove that fer*dr+xydy = f, So*(y– 0)dydr where C is the triangular curve consisting of the line…

A:

Q: 4. Use Green's Theorem of the Plane to evaluate the following closed path integral. xy2 dx+ 2x2y dy…

A: According to green’s theorem closed path integral over the curve C is calculated by,

Q: 15. What is the correct piecewise parametrization of a path C created by starting from C₁ of…

A: Given Path C is C1:  y=x+3,     0≤x≤4C2:  y=x2,         y=7 to y=0C3:  line connecting C1 and C2…

Q: 7. Given the space curve r(t) = (4 sin t,4 cos t, 10t), Find T, N, B, and T(torsion)

A:

Q: 7. let E be the reyion bounded by curve 2+2 in the yex? fint quadant let u xy, Vzy-x d Czry)…

A:

Q: Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points…

A:

Q: VBe. a telisinge change of enrables to evaluae. Hhe gren daule integral Riregron Ahelan bound bou…

A: According to the given information, it is required to use change of variables to evaluate the…

Q: 14. Under the paraboloid z=x² +y2 and above the disk x +y² <9 for (x,y) in the first quadrant.

A: we have to find the volume

Q: Use Green's Theorem to evaluate the line integra Icon (y − x)dx + (2x − y)dy - - for the given path.…

A:

Q: 5. Compute the lenght of the curve u = t, v=0 from t = 0 to t = 1 using the first fundamental form.

A: Suppose, a continuous function is provided over a certain interval. The arc length is the length…

Q: 5. Verify Green's Theorem in the plane for F = (xy + y²)î + (x – y)f and the curve C is as shown in…

A:

Q: Given: Let B (x, y, z) (xz, yz, 3x² - z²). 1. The task is to identify the work done by B on a…

A: Let B→(x,y,z)=&lt;xz,y-z,3x2-z2&gt; A particle going from point (-1,1,-2) to (2,4,4) along the curve…

Q: If you want to test the hypothesis that x is different from 100 with non-parametric test, you write.…

A: Given:  The researcher wants to test the hypothesis that x is different from 100 with non parametric…

Q: 3. WHEN THE LOAD IS UNl FORMLY DISTrRIBUTED ADRIZONTALLY A SNSPENSION BRIDGE CABLE HANGS IN A…

A:

Q: Let Ci be the rectangle with vertices (0,0), (2,0), (0,1), and (2,1) oriented counterclockwise, and…

A: Let C₁ be the rectangle with vertices (0,0). (2,0), (0, 1), and (2,1) oriented counterclockwise, and…

Q: x(t) = t°; y(t) = t® is not a parameterization of the ,3. curve y = x Select one: True False

A: By definition, a function is a special case of a relation between the members of two sets. It is a…

Q: Use Green's theorem to evaluate S,(5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

A: The posted question has multiple questions but according to guidelines we will solve the first…

Q: 13 ABCD is a trapecium with ABDC. A line parallel to AC intersects AB at X at Y Prove that ar…

A: Since you have asked multiple question, As per our policy we will solve the first question for you.…

Q: GIVEN: In Figure 7.24(a), isosceles ARST with RS = RT = 15, and ST = 18; medians RZ, TX, and SY meet…

A: Consider the given figure as

Q: Let C denote the curve of intersection between x = -5z° and y = 6z", starting from A(0,0,0) and…

A:

Q: 1. Given A = (yz + 2r)i + xzj + (xy + 2z)k. Evaluate , A• dr along the curve x +y = 1, z= 1 in the…

A:

Q: (b) Given  = (x²y)î + (xz – z²)f – (xyz)k, determine the following at point (1, 1, 2): (i) V- Â.…

A:

Q: 12. Let H be the hyperboloid where x² – y² + z² = 6. Find an equation for the tangent plane to H at…

A: As you asked only solution for Q12 so, I answered here only Q12

Q: Use Green's theorem to evaluate S. (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

A: According to the given information, it is required to use green’s theorem to evaluate the integral.