Evaluate each line each line integral. dx +(xy-x² )dy where C is the curve y = 9x from (0,0) to (1,3)

Q: Write the linear DE of order one x2dy +(2xy- x+ 1)dx = 0 in standard form + yP(x) = Q(x) or dx + x…

A: Hence option (B) is correct.

Q: Evaluate the line integral y³ ds, for C: x = t³, y = t₁0 ≤ t ≤ 2.

A:

Q: Evaluate | f(x,y) ds where Cis the portion of the curve y = In x from the point (1,0) to the point…

A:

Q: Q. find each line integral along the two given curves C¡ and C2. Sc(x+e') ds (a) C;: x = 1 – 1, y =…

A:

Q: Let w = x? dx + y? z² dydz. Find dw.

A:

Q: Demonstrate that the functions Y1 = a", y2 = sin(x), Y3 = xe* are linearly independent on R. 9.

A:

Q: Let z =e^2x Tany find ((d^2 z)/(dxdy)) and ((d^2 z)/(dydx))

A: Given z = e2xtany

Q: Show that each function satisfies a Laplace equation. 1.ƒ(x, y) = ln sqrt(x2 + y2) 2. ƒ(x, y) = 3x +…

A: A function with of the form f(x,y) is said to satisfy a Laplace equation is it satisfies the below…

Q: Let F = 10xe" i +5x²e® j and G = 10(x – y) i + 5(x + y) j . Let C be the path consisting of lines…

A: According to question given that F→=10xeyi→+5x2eyj→G→=10(x-y)i→+5(x+y)j→C be the path consisting of…

Q: need help evaluating this quesion pls

A: Consider the given information:

Q: ad curl F if F(x, y, z) = xz7i+ 5y¹¹x²j + 6z²yk. d with CamScanner

A:

Q: Construct (a) slope field for the DE: y'+4 y'=x? tabulate the values at these 5 points ( 0,0 )( ±1,-…

A: We have to sketch the slope field of the differential equation y'=x2-4y2. Then we have to sketch the…

Q: Show that each function satisfies a Laplace equation. 1.ƒ(x, y, z) = 2z3 - 3(x2 + y2 )z 2. ƒ(x, y) =…

A: For a function f(x,y,z) to  satisfy a Laplace equation, it has to fulfill the following criteria.…

Q: Evaluate d:/dx on the surface x: + + x²y®=² = 3 at the point (1, 1, 1).

A:

Q: .: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G (x, y) = x³ y² + y² sin…

A:

Q: Determine whether the functions y, and y, are linearly dependent on the interval (0,1). y =sint cos…

A:

Q: xy*dx + x?dy, where C is the le with vertices (0,0), (4,0), (4,5), and

A:

Q: Q. find each line integral along the two given curves C and C2. So(x + y?) ds (a) C: x = t, y = t,0…

A:

Q: Evaluate x*dx C + xy dy, where C is the triangular curve consisting of the line segments from (0, 0)…

A:

Q: (6) Find the integral of the function piecewise linear path from (1,1) to (2,2) to (0,2). b) 22.3…

A: Given the function Fx,y=ey-x,e2x

Q: Draw direction field of the DEQ below, by hand, and sketch an approximate solution curve that passes…

A:

Q: dw Find if w = xy? + x²z+yz?, x = t², y = 2t, and z = 2. %3D dt |t=1

A: Simple derivative problem....

Q: 5. Determine whether the functions y, and y2 are linearly dependent on the interval (0,1). Yi = 1+…

A: Linearly independent of the function. Using Wronskian

Q: Find the differential of each function. (a) y = etan(nt) dy = (b) y = V4 + In(z) dy =

A:

Q: Find the differential of each function. (a) y = etan(rt) dy = (b) y = V2 + In(z) dy =

A:

Q: Show that each function satisfies a Laplace equation. ƒ(x, y, z) = x2 + y2 - 2z2

A: Again differentiating with respect to x, we get Now partially differentiating given function with…

Q: Show that the equation dy/dx=x^2/(1−y^2) is separable, and then find an equation for its integral…

A:

Q: (A) Evaluate" [(x² + y)dx + (x + 1) 1+ along the path ABCA shown in figure C(0,3) A(0,1) x=3sint…

A:

Q: Q. find each line integral along the two given curves C, and C2. So(x + y) ds (a) C: x=1, y = 3t, 0…

A:

Q: Find the differential of each function. (a) y = tan V3t dy = (b) y = 1 + v2 dy =

A:

Q: Find the differential of each function. (a) y = tan(v7t) dy = 4 - v2 %3D y = 4 + v2 (b) dy = %3D

A:

Q: The two functions y1(t) = sin t cos t and y2 (t) = sin 2t are linearly independent. O True False

A:

Q: x = Asin(wt+B); w a parameter, not to be eliminated %3D

A:

Q: use laplace truns form to Solve Y't Y = f(t), y (0) = 0, where

A:

Q: Given z 15 In(t) and y= 225 t then find dy da dy dr?

A: Given that: x=15ln ty=225 t2

Q: Evaluate I = f.(sin x + 9y) dx + (7x + y) dy for the nonclosed path ABCD in the figure. D= (0,9) C А…

A:

Q: Find the linear approximation at x=0 to √17−x. Write your answer in the form y=Ax+B.

A: we have f(x)=17-xDifferentiating both side w.r.t "x"f'(x)=-1217-x-12f'(x)=-1217-xput x=0f'(0)=-1217…

Q: (b) Evaluate (3, 10) J(0, 1) Cto (3x + y) dx +(2y - x) dy along- @ curve y= x? +1; (ü) the line…

A: Given function is 3x+ydx+2y-xdy i) Given curve is y=x2+1 Hence the integrand becomes…

Q: Let y = f(x1, x2, w), where x1 = 2w2 and x2 = w+1. Find dy/dw.

A:

Q: Find the differential of each function. (a) y = etan(t) dy = || (b) y = V1 + In(z) dy =

A:

Q: ) Find dw if w = xe³/², x = t², y = 1 — t, and z = dt 1 + 2t.

A: Topic:- application of derivatives

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

A:

Q: Find dy/dx and d62y/dx62 at the given point without eliminating the parameter. x=1/2t^2+9…

A: Given parametric equations are: x = 1/2t2 + 9 y = 1/3t3 + 4t Differentiating x with respect to t we…

Q: Let z = exsec y Find d²z dxdy and d²z dydx

A: .

Q: Let F = 10xe" i + 5x²e" } and G = 10(x – y)i + 5(x + y) j. Let C be the path consisting of lines…

A:

Q: Evaluate ∮C(yexy−sinx)dx+ (xexy+ 1)dy where C is the path r(t) given by x=t,y=π/2(t−1)2 from t= 0 to…

A:

Q: Find (a) PSD of U(t) = X(t) + Y(t) (b) Sxy (@) and SXu (@) %3D

A: Answer: For the given data, we get