Compute I ds over the path C : ř(t) = (t², 2t, t²) from (0,0,0) to (4, 4, 4).

Q: Let P denote the path that travels along the graph of y = x2 from (0,0) to (1,1). Let f(x,y) = √1 +…

A: Let P denote the path that travels along with the graph of y=x2 from (0, 0) to (1, 1). Let f(x,…

Q: Let A = (1,1) and B = (1,5) be in the Poincar ́e plane. Find C = (xC,yC) for which xC > 1 and…

A: The natural point that comes in our mind is (2,6).

Q: Show that there is no Hamiltonian path inCay({(1, 0), (0, 1)}:Z3 ⊕ Z2)from (0, 0) to (2, 0).

A: Consider the theorem "Cay0,1,1,0:Zm⊕Zn does not have a Hamiltonian circuit when m and n are…

Q: Evaluate ▼ (x² y + x y z²) ·dr where C is the line segment from ( 1, – 1,0) to (2,1,3 Select one: a.…

A: Given integral is

Q: Evaluate where F(x, y) = x² i+(y² – x) j and C is the line segment from (2, 4) to (0, 4) followed by…

A:

Q: Evaluate S2xyzdx + x²zdy + x²ydz over the path c(t) = (t², sin(πt/4), et²-2t) for 0 ≤ t ≤ 2. help…

A:

Q: Let P denote the path that goes in straight lines from (0,0, 2) to (0,1, 2) to (1,1, 2) to (1,0, 2)…

A: Given: F→(x, y, z)=(1-z)5yxez-2z15+14

Q: 14. Calculate | (y? – z)dx + (2ry)dy+(2z-x)dz where C is the path along (t2 + 4t + 2, V4+ 5t, t –…

A:

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

A:

Q: f(x. y.z) = + xy + yz + Q8) Find the Linearization at (1,1.2)

A:

Q: Suppose that a = xdy is a 1 form and Y(v1, v2, v3) = ((v1 – v3)² (v2 – v3)²) ædy what is "a ?

A: Given α=xdy-----(i)γ(v1,v2,v3)=((v1-v3)2,(v2-v3)2)---(ii) To find γ*α------(iii) from (ii) we…

Q: c ls tE line cregmentfoom (3,4,0) to | (1,4,2) computef (zty?)ds&dp

A: The curve C is the line segment from 3,4,0 to 1,4,2. The parametric equation of this curve is given…

Q: — X2 - 4х +

A:

Q: Show that F(z, y) = (ry, z°y?) is not path independent by considering the line segment from (0,0) to…

A:

Q: The set of all linearly independent solutions of D.E yY-y 0 is Select one: a. (1,t,e',e ) b.…

A:

Q: 1. Use the Chain Rule to find u and ou for w = x²y3 where x = dw at s2 +t2 and y = ds

A:

Q: Iculate | y?dx – yz²dy – sen(z)dz, where Cis the path connecting the point A(-2, 2, 4)to the point…

A:

Q: Given a function f(x, y, z) = ryz° +z°yln (z) – z'y? + 4, find: of (1,2, 1) = (1, 2, 1) = (1,2, 1) =…

A: Given problem based on partial derivative.

Q: Consider the curve 7(t) = (-5+ 2t, 5 + 5t) connecting the points (-5,5) and (-4, 7.5). Compute the…

A: consider the following

Q: Use Yule-Walker equations to determine the autocovariance function of a stationary ARMA(2,1)…

A: The autoregressive models for the time series are used for their simplicity and applicability to the…

Q: [1 |A = [a1, a2, a3, a4] 2 11 5 0 3 -1 4 0

A:

Q: Which of these is the correct parametrization of the line connecting (1,2,5) and (0,3,– 1)? A. x =…

A: We know that parametrization of the line connecting pointsx1,y1,z1,x2,y2,z2 is given by x=x1+tx2-x1;…

Q: Consider the linear equalion 5x+2y=17. Fis the value of s that makes the given ordered pair (x,1)

A: The given equation of the line and point is: 5x+2y=17 and Px,y=x,1

Q: (-1,2, 3).

A:

Q: Evaluate (xy + x + 2) ds along the curve r(t) = 2ti + tj+(3-2t)k, 0 st≤ 1. Sc (xy + x + 2) ds =…

A: The solution is shown in step-2

Q: Find Sc((x² + 3y)i + 3y³j) · dr' where C consists of the three line segments from (2, 0, 0) to (2,…

A: Given ∫x2+3yi→+3y3j→.dr→ where C consists of the three segments from (2,0,0) to (2,2,0) to (0,2,0)…

Q: 7. Suppose that T : R² → R² is linear, T(1,0) = (1, 4), and T(1, 1) = (2, 5). What is T(2, 3) ? Is T…

A: