Let P denote the path that travels along the graph of y = x2 from (0,0) to (1,1). Let f(x,y) = √1 + √3y + √x2, and compute ∫Pf ds.

Q: Prove that for any point (a, b) ≠ (0, 0) on the parabola y = x2 , the normal line intersects the…

A: The given equation of parabola is y=x2  For the point (a,b)≠ (0, 0), the slope of normal is and at…

Q: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x +…

A: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x + y…

Q: The mapping $ (y) = fy' : H→H* defined by is not a linear m

A:

Q: (5xy --- 6x(2^

A: Given,        F=(5xy-6x2)i+(2y-4x)j and   y=x3 from the point (1, 1) to (2, 8).

Q: Parametrize the directed line segment which joins the point −2 + 3i to the point 5 − 7i, that is,…

A: The parametric equation on a line passing through the points x1,y1 and x2,y2 is given as follows:…

Q: Show f(x) = e and g(x) = xe linearly independent by finding its Wronskian.

A: Given: fx=exgx=xex The formula to obtain the Wronskian is Wx=f(x)g(x)f'(x)g'(x), where f(x) and g(x)…

Q: Determine whether the work done along the path C is positive, negative, or zero. zero O negative O…

A: We know,       work = ∫cF.dr               = ∫c∥F∥∥dr∥ cosθ    where θ is angle between F and drIf…

Q: Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A:

Q: - (19,8) (10,0) (19,8) ) Show that So fdx + gdy = Sao.0 24x?y dx + 24y2x*dy is independent of path:…

A: Let's find.

Q: Find the Jacobian of following functions f(x,y,z) = 3xy – yz + 2y³z² – 5xyz³ g(x,y, z) = xyz – x³yz…

A:

Q: Show f(x) = e2= and g(x) = x e²z linearly independent by finding its Wronskian.

A:

Q: If after evaluating the Wronskian of the functions y1 and y2 the result is W=7x2+19 in the interval…

A:

Q: 3.2 Evaluate where z = x + iy with y the path on line from z = 2+i to z = 1 + 2i.

A:

Q: Find a path c(t) that traces the line y = 2x + 1 from (1, 3) to (3, 7) for 0 ≤ t ≤ 1.

A: Given:

Q: 3. Use Green's Theorem to evaluate G³ï+xj)•dr around the perimeter of the rectangle 0<x<2,0<y<3.…

A: Given ∫C(y2i+xj).dr We know that dr = dxi+dyj Thus ∫C(y2i+xj).dr = ∫C(y2i+xj).(dxi+dyj)  =…

Q: Determine whether the work done along the path C is positive, negative, or zero. y O positive…

A: Consider that the sign of the work depend on the orientation of the path C. here the circulation can…

Q: Let D, be the linear transformation from C'(a, b] into C[a, b]. Find the preimage of the function.…

A:

Q: Show that the function f(x, y, 2) = (x² + y² + 2e**)4 is strictly convex on R³.

A:

Q: Find the image of the line y =-x under the mapping = f(z) =2² + 4z %3D %3D

A: We need to find the image of the line y = - x under the given mapping.

Q: Find the orthogonal trajectories of the family of circles passing through the points (1, −2) and (1,…

A: Given that

Q: Prove that the following curves are intersecting with a right angle: 5y-2x+ y -x²y =0 2y+5x+ x* –…

A:

Q: The gradient vector of the function f defined by f(x,y)= In(1+7x² +5y²) is equal to Select one: O…

A:

Q: Compute the discriminant D(x, y) of ƒ(x, y) = x2y2.

A: fx, y=x2y2 Partially differentiating with respect to x, we get ∂f∂x=2xy2 Partially differentiating…

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: 26. Let F(x, y) = (3x + y, a?y) and let C be the path along ry = 2 from (1, 2) to (2, 1). Calculate…

A:

Q: Determine whether the work done along the path C is positive, negative, or zero. y

A: The work done along the path C is

Q: Find the exact length of the curve. y = In(1 - x²), o s x s

A: Solve the problem using definite integral

Q: Verify Green's Theorem for: f4y³dx-2x²dy where C, oriented anti-clockwise, is composed of the…

A: To find the integral ∮C4y3dx-2x2dy where C is the positively oriented closed curve x2+y2=9, y≥0 and…

Q: Find the bounded อน əx solution of อน 2 + U if U(x, 0) = 6e-3x. at

A: We have ∂u∂x=2∂u∂t+u  The initial condition is ux,0=6e-3x Now, ∂u∂x=2∂u∂t+u can be written as…

Q: . Use the method of Lagrange multipliers to show that for x, y > 0, we have a" +y" > (팔1)" 2

A: We will first try to minimise (xn + yn)/2 using Lagrange multipliers then show that its minimum…

Q: Let C be the piecewise-linear path from (0, 0) to (1, 0) to (0, 1) to (–1,1) to (–1, –1) to (0, 0),…

A: I have applied stokes theorem,  please rate and feel free to ask any query about any part. Thanks

Q: Let C be the line segment connecting 0 to ni. Then f. 1-e2z dz =

A: we have to find integration

Q: Use the Path Length formula to find the path length of the function over the given interval. Path…

A:

Q: The area bounded by the curve y = 4r and the lines z = 2 and I=8 above the I- aris is O 240.00…

A:

Q: Determine whether the work done along the path C is positive, negative, or zero. c/

A: we know that Work W=∫C F→·dr→

Q: • Verify that 3r is a one-parameter family of solutions of the DE ry + y = 3r. • Deduce a solution…

A:

Q: Show that f(-ydx + xdy) where C is the line segment joining (x, y) and (x₂, y2).

A:

Q: Evaluate (x-y+z-2)ds where C is the straight-line segment x=t, y= (1-t), z=1, from (0,1,1) to…

A:

Q: Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: Dx(f)=8x+5 Apply integration both side  ∫Dx(f)dX=∫(8x+5)dx   f(x)=(8x2)/2 + 5x +c (here c is the…

Q: Determine whether the work done along the path C is positive, negative, or zero. /c/ zero negative…

A: For calculating the work done from the field we will have to see the direction of both vector field…

Q: Find the Jacobian of following functions f(x,y, z) = 3xy – yz + 2y z2 - 5xyz3 g(x,y, z) = xyz -…

A:

Q: Determine whether the work done along the path C is positive, negative, or zero. negative positive…

A: Consider the provided graph, Determine whether the work is done along the path c is positive…

Q: Consider the path r(t) = (4t, 2t², 2 In t) defined for t > 0. Find the length of the curve between…

A:

Q: 5. Show that the following orthogonal families of curves: are x² + y² : = ax, x² + y? = by

A:

Q: Show that Si2 f dæ + g dy + h dz = S - (4xy³z*dx + 6y?x?z4dy + 8z°y³x²dz) is independent of path:…

A:

Q: Compute the convolution y(n) = x(n) * h(n) , Where x(n) = {1,1,0,1,1} and h(n) = {1,-2,-3,4} , Using…

A: Given: Given convolution expression is Y(n)=x(n)*h(n) x(n)={1,1,0,1,1} h(n)={1,-2,-3,4}