Integrate f(x, y) = y(x² + y³) 3 over the domain x² + y° < 4, with y > 0.

Q: dz Use the Chain Rule to find dt for z = x2 + y2 + xy,x = sin t , y = e'.

A: z=x2+y2+xy ; x=sint , y=et

Q: Find the differential dy: y = In (sec² (3ª²–2x+5)).

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Q: Inx dx, 2. Integrate (1) using the substitution u = In x (ii) using integration by parts.

A: Integration by substitutions and by parts

Q: Find the first partial derivatives of the function. 4x – 7y f(x, y) = %3D 4x + 7y A(x, y) = Wx, y) =

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Q: Find the differential dy. y = 5x2 / x-9       dy =

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Q: Find the differential dy, then evaluate: y= 2x3+ 6x-| when x= -2, dx= 0.l

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Q: integrate ƒ over the given curve. ƒ(x, y) = x3&gt;y, C: y = x2/2, 0 &lt;=x&lt;= 2.

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Q: Find the partial derivatives of the function f(x, y) = integral from x to y of cos(-6t^2 + 2t -…

A: Given: To Find: The partial derivative of f(x,y).   Fundamental Theorem of Calculus:

Q: obtain the particular solutions satisfying the indicated conditions: dx/y=(25-x^2)^-1/2dy; y(0)=1

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Q: Find the differential dy. (a) y = xV7-x dy (b) y = (1+x) dy

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Q: dz Use an appropriate form of the chain rule to find dt z = 8x"y³; x = t°, y = t Enter the answer in…

A: Topic :- Differentiation

Q: Find the second-order partial derivative. Find fy 2x. when f(x,y) = 8x y-7y+ 3. xy O A. 48xy O B. -…

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Q: I-x² f (x, y, 2) dz dy dx 1-x² Jo

A: we have to find the region of integration

Q: (1) Use the Chain Rule to find dz/dt. (a) z = r² + y² + xy, r= sint, y = e'. z = x2 +y?, x = cost+…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Given f(x, y) = 11x²y then the total differential df = %3D 11xy dx + 11x² dy 2xy dx + x² dy 22xy dx…

A: The function is given by fx,y = 11x2y To evaluate : The expression of the total differential df

Q: Find the integrating factor a. (xy+y2)dx+(x2+3xy)dy=0   b. (y2e2x+1)dx+(2ye2x-ex)dy=0

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Q: Find all second partial derivatives of the function f(x, y) = xy + x° + y at the point xo = (2,4). =…

A: Consider the case of a function of two variables, f(x,y) since both of the first order partial…

Q: Use a suitable method  to find the solution of (1-x^2)(1-y)dx=xy(1+y)dy

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Q: For f(x,y,z)=3xy+2y+8z - cos(x²+y²–z), the partial derivative fxy(1,2,5)=

A: Given function is fx,y,z=3xy+2y+8z−cosx2+y2−z. We have to find the partial derivative fxy1,2,5.…

Q: Find the differential dy. (a) y = xV10 - x dy = -2 (b) y = (1+x) ? dy =

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Q: Compute the partial derivative: f(x, y) = sin(x" –- 3y) fy(0, ) =

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Q: Obtain the solution using Integrating Factors Found by Formulas a.)  xydx − (x2 + 2y2)dy = 0

A: I am attaching image so that you understand each and every step.

Q: 1 -dt = xy ndif y + J sint+1 secx dx

A: Since you are asking multiple questions. As per our guidelines, we are supposed to answer only one…

Q: Find the I.F of 2y(x^2-y+x)dx+(x^2-2y)dy=0

A: Please see the answer below

Q: [-+] 5t dy 3.1는-51%3D-y dt

A: This is a linear 1st order differential equation.

Q: solve using ODE from t=0 to 2 when y(0)=1 dy/dt= yt^3 - 1.5y

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Q: Compute the partial derivative and evaluate at the given point. (a) f(x, y) = 3x?y + 4x³y? – 7xy4,…

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Q: Integrate f(x,y) = x-5y over the curve C: x +y = 64 in the first quadrant from (0,8) to (V32,/32).…

A: Formula Used:Line integral ∫Cf(x, y) ds=∫abf(x(t), y(t)) dxdt2+dydt2dt

Q: Find the all the 1st order partial derivatives of the function f(x, y,z)= Vx² +z-2 + sin

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Q: Given that e2y, 10x2+4. f (x, y) = sin Enter a 10 significant figure approximation to the partial…

A: We will use matlab to find the answer

Q: integrate ƒ over the given curve. ƒ(x, y) = x + y, C: x2 + y2 = 4 in the first quadrant from (2, 0)…

A: We have to find the integral The parametric equation of given curve is

Q: %3D y"(t) = 4y(t) – e-tU (t – 1), y(0) = y'(0) = 0.

A: Solution

Q: Find all the second-order partial derivatives of the function. r(x.y) = In (2x + 3y) дудх дхду dy?

A: Given that r(x,y) = ln(2x+3y) We need to calculate all the second order partial derivatives. The…

Q: Find the differential dy. (a) y = xv8- x %3D dy %3D (b) y = (1+ x)7 dy

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Q: F(x, y)= x²y?

A: Consider the function  s=f(p, q),here p and q are independent variables and s is a dependent…

Q: Use the Chain Rule to calculate the partial derivatives д(т, у) — sin (т? + у?), х— 4и — v, у — —…

A: Given g(x, y)=sin(x2+y2) ,x= 4u-v and y=-(2u+2v)

Q: Q4. Find dz/dt where z = 2xy - x² y² and x = 2t, y = t²

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Q: Find In(y') at the point (0, 1/e) where xy° – In(xª + y) = 1.

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Q: se the Chain Rule to find dw/dt. w = INVX2 + y2 + z² x = 9 sin(t

A: Here we have to use the chain rule to find dwdt=? w=lnx2+y2+z2, x=9sin(t), y=3cos(t), z=5tan(t)

Q: dz Use the Chain Rule to find : z = = cos(x + 4y),x = 5t*, y = - %3D dt

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Q: Find the linearization of x = -1 f(x) = 3+ S sec(t – 1)dt at

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

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

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Q: Find the second partial derivatives of the function f(x,y) = x°y° + 2x°y. 1. 2. 3. dxdy a² f 4. dy?…

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

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Q: Find the second order partial derivatives дхду of and дудх f(x,y)= 4x² + In x + e*** – cosy +9y +3.

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Q: Find the integrating factor of : 2y(x2 - y+ x )dx + (x² – 2y)dy = 0 ху O y 2х e2x

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Q: What is the integrating factor of the nonexact DE (4xy + 3y – x) de + æ (x + 2y) dy = 0?

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