Verify Green's Theorem by evaluating both integrals L v? y2 dx + x2 dy = dA ду ax for the given path. C: square with vertices (0, 0), (9, 0), (9, 9), (0, 9) L y? dx + x2 dy = - x² aN ƏM dA = ду ax

Q: If the substitution u = √x + 1 is made, the integral 3 A S u² u² - 1 du B du 3 2u²2 u² - 1 √ √x+1 dx…

A: We solve the given problem by using the substitution method.

Q: 2. (у? — 2ху + 6х)dx — (х? — 2ху+ 2)dy %3D 0, whenх%3D 1,у %3D2 = 3. v(2uv? — 3)du + (3и?v? — Зи +…

A:

Q: Transform the equation: 2x2y'' + xy' + 3y = 0 to the form of: a(d2y/dz2) + b(dy/dz) + cy = 0 (a,…

A:

Q: (x+y)^2=x^2 + 2xy + y2, subsitute (-2) for x,and (-1) for y, and check if the left hand side is…

A:

Q: Find the S(x* +) dx xe-1 А. 1x? + c e-1 4e xe+1 В. Ix2 + c e+1 2e xe+1 С. 1x3 + c e-1 Зе xe+1 1 D.…

A: Given query is to find the derivative of the expression.

Q: ?w Əv у Find when u = 0, v=0 if w=x² + ₁ x=6u-2v + 1₁ y=u+4v - 1.

A:

Q: Show that D^2 = {(x, y) ∈ E^2: x^2+y^2 ≤ 1} ⊂ E^2 and the space containing a single point are…

A: In algebraic topology, two topological spaces are said to be homotopy equivalent if there exists a…

Q: ...,N, becomes Y = a, + a,X. Q6. (a) If the least square line of points (xţ, Y1), i = 1,2, ... ..…

A: We are given the following equation To calculate the slope parameter a1  the formula is To…

Q: +タ x2 – 1

A:

Q: ∇×F=?   -24xz is incorrect！

A:

Q: əz əz 1. Let z = x² + y³, x = 2st and y = s − t². Compute for and əx Ət

A:

Q: Find дхду of z = In(x² – y) %3D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: 3. Suppose X~ Bin(4,2/3). Let Y = 2X+1. Find py (y), and fill out the table below. You may not need…

A: Ans#- Given, X ~ Bin4, 23. Let Y = 2X + 1            Find PY(y)        We know, In the binomial…

Q: Solve for x: xy2 + yz2 - 4 = 2x - 1. 3-yz2 b) х %3D у2-2 a) x = *y^tyz2-3 2 с) х %3D 3 — yz2 -у? +2…

A: Consider the given expression.

Q: x³y³dy у2— 4у-21 (x – x4y)dy + (y + x³y²)dx :

A: See the solution and follow the step.

Q: 2. Find the equation of the place that pusses + through the point= (-1,2,1) Contains the line of…

A:

Q: дz дz If z = f(x, y), find a and for the following equation əx ду z = x² + 3xy + y³

A:

Q: Find the differential of w = ln /x² + 3y² + 2z²

A: Here we use chain rule of differentiation to find the required differential. According to chain rule…

Q: Consider the equation x² + y³ + zª − 8xyz = z². Find z point (1,1,1). at the

A:

Q: ди ди x====u+Yay ?х

A:

Q: d) Let g(x,y) = (3x + y)2(2y + 1) and h(x, y) = 6y2(2x + y) h i) Find дх’ ду’ дх’ ду

A: The given functions are  and

Q: Find two linearly independent solutions of 2x²y" - xy + (-4x + 1)y=0, x > 0 of the form y₁ = x¹(1+…

A:

Q: дz дz 45. Find and Әх ду at (-1, 1, -1): yey-x² +z² = -3z-y²³

A:

Q: Find two linearly independent solutions of y" + 3ry = 0 of the form Y1 = 1+ a3x³ + a6x® + · .. Y2 =…

A: We find two linearly independent solutions of the given differential equation  y"+3xy=0.......(1)

Q: дz Find and əx дz ду' yz + x ln y = z²

A: Given query is to find indicated partial derivatives.

Q: Find the e v

A:

Q: Solve the following differential equation: yde+xdy 1-x²y² +ædr=0. = constant.

A: Given that the differential equation ydx+xdy1-x2y2+x dx=0

Q: The ordeng and transportation Cost C Cin hundred of dollars) for automobrle dealership is modeled by…

A:

Q: y = Arccot x 2 Arccot /x Vx(1+x) А. Arccot x С. x* +x Arccot x Vx(1-x) Arccot x Vx(1+x) В. D. -

A:

Q: Let x = (m , 1 , 0 , -2)", m > 0 and ||x|l2 = v30, then m = Select one: а. 4 b. 5 с. 6 d. 7

A:

Q: Calculate zu for: z = 3x² - 2xy + y², x = 3u + 2v, y = 4u − v.

A: To calculate zu for: z=3x2-2xy+y2, x=3u+2v, y=4u-v

Q: f of If dx + In(7y), what is ? - дхду Select one: 1 7. а. дхду y y b. дхду - y + 7e?y С. дхду 1+e7y…

A: Option E is correct.  Make x constant

Q: 1. If R=x²y i-2y²zj + xy²z²k, find a²R at the point (1, -2, 1).

A:

Q: solve in terms of Tf

A:

Q: 3. Let 7, r, and r, be the roots ofx' +3x-5x-4= 0, construct the equation whose roots are: 7(r, +r3…

A: