2 2 !(GHC)). i+ y xy² Evaluate the integral joining (2, 1) to (5, -3). Enter an exact answer. Provide your answer below: Alimits_c( [] + [-]¹) ) i dr = j. dr using the potential function f(x, y) = 2 xy where C' is any curve

Q: Find the solutiTon of followina ordfnarg differentral equation -2x

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Q: given f(z)=u(x,y)+iv(x,y) is an analytic function where u(x,y)=x^3-3xy^2. find f(z)

A: We have to find .

Q: Let  f(x, y) = sin(15x2 + 3y2) Calculate the quadratic approximation of f at the point (0,0)

A: Given that,  fx, y=sin15x2+3y2 The quadratic approximation of the function fx, y at the point x0, y0…

Q: 2. a). Find the velocity and acceleration of a particle whose position function is x(t)=…

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Q: x3 dx (x – 1)5 y = Select one:

A: First evaluate the integral by substitute method. Then apply the limits of integral.

Q: Find a potential function for F. f(x,y,z) =

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Q: Find V· (V × F), if F(x, y, z) = 3e**i+3xe'j – 3e²k. - V·(V × F)

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Q: Use differentials to estimate the change in f (x, y, z) = x² In(5yz + 1) as (x, y, z) changes from…

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Q: An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y) + iv(x, y).…

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Q: 2. Determine the directional derivative of o(x, y, z) = re" + y² + xyz at the point (2, 0, 3) in the…

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Q: Determine the order of the DE. a.) y' + y = 5y^2 b.) (dy)/(dt) = t c.) y' = y'' + 5t^2

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Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 15x from (15, 15) to (0,0). NOTE:…

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Q: Integrate the function. S dt o. O. V6-R+ sin'1 6t + C 6t o. + C 612 o. 6t 16-12

A: We can find the integral as below.

Q: Find a potential function for F(x, y, z) = :yi+xj+xzk or prove none exists.

A:

Q: Calculate the line integral [F•dr, where F = 3x°yi + x'j in two cases for C1 and C2. These two…

A: The given vector is F=3x2yi+x3j Here we use Green's theorem. So the Green's theorem is…

Q: Find the implicit equation of the tangent plane to z = e + x + x² + 12 at the point (6, 0, 55).

A: Given: z=ey+x+x2+12 Point (6,0,55)

Q: Suppose F(x,y)=. Use Green's Theorem to calculate the circulation of F around the perimeter of the…

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Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

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Q: af Calculate at point (-1,2) where f (x, y) = 8+ x² + 3y? dv and v = i+j. 10 2 5/2 V2

A: fx, y=8+x2+3y2  &  v=i+j Partially differentiating with respect to x, we get fxx, y=0+2x+0=2x…

Q: Find the potential function for F(x,y,z) = (x^-1z)i + (y^-1z)j + ln(xy)k. Show all steps and explain

A: Potential function of  F, is f such that ∇f=F.

Q: OLif f(x, y,z)=2exp(-5xyz)cos(15z) Find

A: Partial derivatives

Q: Find the quadratic approximation at (0,0) for f(x,y) = ln(1+x^2 + y^2).

A:

Q: Solve the partial differentiabion equation +6.0 = 2-y Ox Show that the gereral aoludion 2.

A: Given. the partial differential equation                            ∂2z∂x2+5∂2z∂x∂y+6∂2z∂y2=2x-y…

Q: 7. Let x² - y² 2xy '(x² + y²)²¹ (x² + y²)²) when (x,y) # (0,0). a) Determine the potential o to F…

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Q: Draw a direction field for the equation y'=y+x-y^2 for -5 < x, y

A: The direction field is obtained as follows:

Q: Use the substitution u=-3x+2y to solvethe differential equation (-3x+2y) y'= - 1. a) Clearly…

A: Given differential equation is: -3x+2yy'=-1. Let, -3x+2y=u. Differentiate both sides w.r.t. x.…