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

Q: 4. Evaluate fe fds where f(r, y, z) , ) and 0 <t< 1. = 12r2 and the path C is given by r(t)

A:

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: Suppose that T : R2 --&gt; R2 is linear, T(1,0) = (1, 4), and T(1, 1) = (2, 5). What is T(2, 3)? Is…

A:

Q: Letr(t) = (t2, 1- t,4t).Calculatethederivativeofr(t) • a(t)att = 2, assumingthata(2) = (1,3,3)…

A: Given that, rt=t2, 1-t, 4t a2=1, 3, 3a'2=-1, 4, 1 Need to evaluate derivative of rt.at

Q: 12 3. If u lx + my, v = mx-ly, show that ди 4 + m

A:

Q: 1. Show that S, has the presentation (x, y|x² = y = (xy)² = 1). %3D

A: The symmetric group S3 is given as S3=I, 1 2, 1 3, 2 3, 1 2 3 1 3 2 where  I=123123, 1 2=123213, 1…

Q: Evaluate / (x - 2y + z) ds. S: z = 3 - x, 0sxs 3, 0sys 2

A:

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

A: Given path is:

Q: Find the fowien senies fon | X), -T<X <A

A:

Q: Suppose ƒ(1, 2) = 4, ƒx(1, 2) = 5, and ƒy(1, 2) = -3. Find the linear approximation to ƒ at P0(1, 2,…

A:

Q: 3. Find all the fixed points and classify cach of them: f(r,u) ryev,

A: Solution:- Fx,y=xye-x2-y2 Put Fx=0 and Fy=0 Fx=e-x2-y2y-2x2=0and Fy=y-2y2 e-x2-y2=0 So,  0,0,12,12,…

Q: of is: If f(z, y, z) = ry z' + In (z) In (y²) In (z³) then dz

A:

Q: a. Let C = C, U C2 where C, is the line segment from (2,0,0) to (3,4,5) and C2 is the line segment…

A: c1: Line segment from (2,0,0) to (3,4,5)The equation is…

Q: Q1. Compute xdx x'+10 using trapezoidal and Simpson's 1/3 rules with the number of points 3 and 5.

A: The given integral is, I=∫01xdxx3+10 Dividing the interval (0,1)  into 2 intervals (for 3 points)…

Q: Compute x 2z ds where C is the line segment C from (0,6,–1) to (4,1,5).

A: The given line segment from   to   can be represented parametrically as: , , and , for    Using the…

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: Show that 6.8) fdx + gdy = Jc.8) (12,16) • (12,16) - (28x³3 By³dx + 35ytx dy) is independent of…

A:

Q: Compute ∇ƒ(-1, 2, 1), where ƒ(x, y, z) = xy/z.

A: Given,f(x,y,z)=xyz     As we know ∇f(x,y,z)=∂f∂x,∂f∂y,∂f∂z

Q: Compute I ds over the path C : ř(t) = (t², 2t, t²) from (0, 0,0) to (1, 4, 4).

A:

Q: Compute Jx²z ds where C is the line segment from (0,6,–1) to (4,1,5).

A: The objective is to compute ∫Cx2zds where C is line segment from  0,6,-1 to 4,1,5

Q: Let w = -4xy – 5yz – 4xz, x = st, y = et, z = t Compute (3,4) = as (3,4)%3D at

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Q: Find the angle (in DMS) between the line L1 through the points P1(2, 1, 4) and P2(–1, 4, 1) and the…

A:

Q: 2 let C be an arbiterery curve from l0,0) to D). (2,4) Evala vute: (3x² oy, x-2)- dio

A: To find the value of the given line integral.

Q: 3 4 Let y = -7 and u = -6 -4 1 Compute the distance d from y to the line through u and the origin. d…

A: The projection of a vector on a plane is its orthogonal projection on that plane. In simple words,…

Q: (2) Let P = (1, 1), Q = (4, –2) and R = (2,3). Find the point S such that R$ is equivalent to PQ.

A:

Q: xy−5yz−7xz,x=st,y=e^(st),z=t^2 Compute ∂w/∂s(1,−2)=

A: The equation given as  w=-2xy-5yz-7xz , x=st , y=est ,z=t2. The partial derivative of the function…

Q: Compute S S SB r dxdydz, B = [0, 1] × [0, 1] × [0, 1]. (Answ: 1/3)

A: We are given B=[0, 1]×[0, 1]×[0, 1] to compute ∫∫∫B x2 dxdydz

Q: 2. Compute Ja F · ds for F c(t) = (t , In(1+ t²), e*) for 0 <t < 1 VV, where V(r, y, z) = 4x² In(1+…

A: Find your answer below

Q: if T(x,y) = (x,0) then Null(T) = span{(0,1)} Select one: True False

A:

Q: 3. a) Compute : ♫ (Re z − 3z) dz where ♪ is a directed line segment from z = 0 to z = i.

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

Q: When is S \ T = T \ S for sets S, T?

A: Given that two sets S and T. The definition of S\T=a∈S,a∉T and T\S=b∈T,b∉S. Here, neither of these…

Q: Q1. Compute xdx x' +10 using trapezoidal and Simpson's 1/3 rules with the number of points 3 and 5.

A: we have  I=∫01x dxx3+10dx  n=3h=b-an=1-03=13…

Q: If S e-t)rLnt dt, Find the valae of (n)

A:

Q: 2.4. Compute and plot y[n] = x[n] * h[n], where %23 1, 3 s n < 8 0, otherwise x[n] = 1. 4 s ns 15…

A:

Q: Show that f10 fdx + gdy = S6 10 5a*y²dx + 2yx³dy is independent of path •(11,–7) ,-10) • (11,–7)…

A:

Q: -6 3 Let y = -5 and u = -4 -2 Compute the distance d from 3y to the line through u and the origin.

A:

Q: 32. Let y = (1, 2, 6) and u = (1, 1, 1). Compute the distance from y to the line through u and the…

A: line through u(1, 1, 1) and v(0, 0,…

Q: et whose A = T be standard matsix teans bormaton is the lineas 2. 3. Does maps R3 onto R4? s Ta one…

A: Given that T is a linear transformation whose standard matrix is given by A=203032005000. We have to…

Q: graph the points z = x + iy that satisfy the givenconditions. | z |&gt; 2

A: Complex numbers

Q: Let C be the straight line path from (0, 1, 2) to (2,0, 5). 1. Compute ſo ry ds. 2. Compute fc x dr…

A:

Q: Evaluate F dr where F(x, y, z)= (x', y’, xyz) and C is the line segment from х, у, со (1, 4, 3).

A: Use parametric to solve

Q: 2) Evaluate yzdx+ xzdy + xydz where c is the line segment from (1,1,1) to (3,2, 0).

A: Given: c is a line segment joining 1, 1, 1 and 3, 2, 0. To evaluate: ∫cyzdx+xzdy+xydz

Q: Compute I ds over the path C : F(t) = (t, 2t,ť²) from (0,0,0) to (4, 4, 4).

A: The answer is given below:

Q: Suppose A=LU. Find t, where: 1 0. 01 [2 3 4 L = 1 0. U = [0 3 1 5 3 01 0 0 1 3 0 4 and A = 1 8. 10 t…

A: given that A=LU…

Q: 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: Given,

Q: Show that (t) =| 2 3t is the fundar

A: Given that,            y'=A(t)y                          ...(1) where                A(t)=-1t1-6t23t

Q: Suppose z = f(x,y) where x = Puv and y=u+tv². Given that z,(4,3) = 4 and z,(4,3) = – 1. Compute z,…

A: Explanation of the answer is as follows

Q: Wq = (12,3), wz=(1,3,5) not; where Determine the and w- (15,9) span R (15) span TR oY V (2,7,8).

A:

Q: If f = ux+v-y, g=u²+vy+ w and O(f.g,h) ô(11,v, w) h= zu -v+ vw compute

A:

Q: Compute / (1/zy, 1/(z + y)) dr along the path from (1, 1) to (3, 1) to (3, 6) using straight line…

A: The parametric vector form of a straight line from (1,1) to (3,1) will be given by:…