(x,y) = xy i + x+15 yj, on R'. Find a potential function for

Q: Find the total differential. w = x7yz9 + sin(yz) dw = 7x°yz° dx + 6.9 7_9 +2 cos (yz) )dy + (9x'yz°…

A:

Q: Show that [ xdhy – ydy c Vx*+y² is independent of any path of integration which does not pass…

A:

Q: Evaluate the line integral (8x + 7y)dx + (2x - 7y)dy along the curve C: a = 8 cos t, y = 16 sin t (0…

A:

Q: If f(x, y) = 2x² – 8y², then the total differential of f at x = 1 and y = -2 is : - O df = 32 dx + 4…

A: In total differential take the derivative of each terms, put the given values and simplify.

Q: Find the partial integral. + 3y?) dy t.

A: Given that a  integration and we solve this integration by using general formulas of integration. We…

Q: If f(z, v) – 4z°y+ 8zy, then the total differential of f at z-1 and y - 1is: O df - 17 dz + 22 dy O…

A:

Q: V24z – 2z3 dz dy dæ, by changing the order of integration to dæ dy dz.

A:

Q: Let y = tan(2z + 3). Find the differential dy when z = 2 and dæ = 0.4 Find the differential dy when…

A:

Q: Use Green's Theorem to evaluate the line integral. ex cos(2y) dx – 2ex sin(2y) dy C: x2 + y2 = a²

A: Use Green's theorem

Q: y, thên thế total differential of and y O df = 11 dr + 16 dy O df = 15 dr + 19 dy O df = 12 dr +18…

A:

Q: 1. 3(3x2 + y²)dx – 2xydy = 0

A: According to our guidelines we can solve only the first question. Please re post the other questions…

Q: (3) Evaluate the line integral of the first type fez2 ds, where C: x = cost y = sint where 0 ≤ t ≤…

A: As per the company rule, we are supposed to solve one problem from a set of multiple problems.…

Q: Find dz/dt where z = 2xy - x² y² and x = 2t, y = t² at t=1

A: I have solved the problem with two methods.Final solution is in the box.

Q: Evaluate the line integral / (7x + 5y)dx + (3x – 9y)dy along the - curve C: x =2 cos t, y = 4 sin t…

A:

Q: -dx. V1–16z² Consider For the u-substitution u = 1 – 16x², which is the new integrand in terms of u?

A: Given:-∫014x1-16x2dxTo find: new integration in terms of u by using the u-sbstitution, u=1-16x2

Q: Find a homogeneous (linear) DE with a following FSS: y1(x) := 1; y2(x) := sin(5x); y3(x) := cos(5x)

A:

Q: If f(x, y) = 4x² – 6y², then the total differential of f at x = 1 and y = -2 is : O df = 24 dx + 8…

A: df=dx+dy (see step 2).

Q: Find the work done by F(x, y) = (x, Y) over the curve r(t) = (e' cost, e' sin t) (x² + y?)3/2 from…

A:

Q: What is the integrating factor of the linear DE of order one ydx + (3x - 2y +5) dy=0,

A:

Q: Use the Chain Rule to find dw/dt. In(Vx² + y² + z² ), x = 3 sin(t), y = 5 cos(t), z = 6 tan(t) W =…

A: We have to find the derivative  using chain rule.

Q: Solve by Laplace transforms. y – 3 | y(T)dr = 4e' sin(2t). %3D 0,

A: by Applying Laplace transformation and inverse Laplace transformation we get the answer

Q: 3. ) Compute for the increment of the function f(x,y) = *+3y . Also, find the total differential of…

A: w = f (x, y) and let ∆x and ∆y be increments of x and y respectively. The increment ∆w of w = f (x,…

Q: Write the approximate change formula for a function z = ƒ(x, y) at the point (x, y) in terms of…

A: Consider the following function: z=fx,y

Q: Evaluate the line integral (5x + 8y)dx + (3x – 5y)dy along the - curve C : x = 10 cos t, y = 20 sin…

A:

Q: Let y = 5,a. %3D Find the change in y, Ay when r = 5 and Ar = 0.2 Find the differential dy when r =…

A: Our problem is let y=5√x First, it is easiest to take the derivative of this when in a different…

Q: Use the Chain Rule to find dw/dt. w = In Vx2 + y2 + z2 ), x = 4 sin(t), y = 6 cos(t), z = 5 tan(t)…

A:

Q: Use the direct method to evaluate the path integral for the work done by F(x, y) = (y, -x) along…

A: -4π

Q: If f(r, y) = 3x2 – 8y, then the total differential of f at z = 1 and y=-2 is: %3D O df = 6 dx + 32…

A: we can find the total differential as below using the properties of partial derivative

Q: Use the Chain Rule to find dw/dt. w = In Vx2 + y2 + z2 x = 2 sin(t), y = 5 cos(t), z = 4 tan(t) dw…

A:

Q: (a) Find the differential dy. y = V 24 + x2 dy = V 24 +x?

A:

Q: Vy+I ydx dy -1 -Vy+1

A: Let's find.

Q: Use the Chain Rule to find dz/dt. z = x2 + y?, x = cost + sin t, y = cos t – sin t. -

A:

Q: Let z(x, y) = 2x2 3y2 where x = 2s – 4t & y = 9s + 8t. | dx dy ду az Calculate ds dz & and using the…

A: We have to find all first order partial derivatives.

Q: What is the value of the line integral ∫AB xy dx defined by the line y = x +2 and it is along the…

A: The given problem is to evaluate the line integral along the path y=x+2 from points A(0,2) and…

Q: The time rate of change of liquid circulating in two tanks is govemed by dy -0.02x + 0.02y, = 0.02x…

A:

Q: Assume that a body moving with velocity v encounters resistance of the form dv/dt = -kv3/2. Show…

A:

Q: Evaluate the line integral (6x + 8y)dx + (3x – 3y)dy along the curve C: x = 4 cos t, y = 8 sint…

A:

Q: Find the total differential. w = e3Y cos(5x) + z5 dw

A: The total differential of a function w= f(x,y,z) with continuous first partial derivatives in a…

Q: e for (2x + 1) cos(x) dx. 14. Use integration by parts to evaluate

A:

Q: Find the differential of f(x, y) = vx2 + y³ at the point (1,2). df

A:

Q: Solve the differential eavations ydx xdy = 0 x' +y° +y?

A:

Q: If f(x, y) = 4x²y+7xy°, then the total differential of f at x = 1 and y = 1 is : %3D O df = 15 dx –…

A: Use formula of total differential

Q: Given z = 3x'y + V5 cos 2y-2x, detemine the total differential o

A:

Q: What is the integrating factor of (ry + y) dr + (r + 2y-1) dy %3D

A: Given xy+y2dx+(x+2y-1)dy=0Compare above differential equation with…

Q: Supply the missing integrand and limits of integration. 5 a) S S,2 6x²y dxdy = dy -5 сx/2 b) S S²…

A: We have to find the missing integrand and limits of given integration.

Q: 1 find the total differential dz. z=xsin y + x² z = (2x² + 3y)² z=5x-7y

A:

Q: Find the total differential of w ze(z+y) at (0,0, 1).

A:

Q: What is the integrating factor of 6y²dx – x (2a + y) dy Oy-2 Oy? Oy

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.