2. As an application of partial derivative of multi-variable functions, provide one page abou Lagrange Multipliers and explain the application of it with an example.

Q: Evaluate the indicated partial derivatives. f(x, y) = 3.x°yey af8,2) (3,2) af8,2)

A: The given function is:fx, y=3x5yexyTo find ∂f∂x3, 2 and ∂f∂y3, 2

Q: How is linear approximation used to approximate the value of afunction ƒ near a point at which ƒ and…

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Q: 12. Obtain the family of curves which represent the general solution of the partial different ial…

A: The general solution of a partial differential equation P(x,y,u)ux+Q(x,y,u)uy=R(x,y,u) is calculated…

Q: 7. Use the method of Lagrange multipliers to find a relative minimum of f(x, y, z) = x² + 4y + 16z…

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Q: дх

A: 27. z=x7+2y+xy ∂z∂x=∂∂xx7+2y+xy        =7x6+0+yxy-1        =7x6+yxy-1 And ∂z∂y=∂∂yx7+2y+xy…

Q: 4) Find the orthogonal trajectories of the family of curves

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Q: Example 2 : Form the partial differenial equation by eliminating arbitrary function from z= f(y/x).

A: We have given function z= f(x/y)  We have to form the partial differenial equation by eliminating…

Q: 2+ yety y' : 2у - хеху

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Q: Find both first partial derivatives. z = 14y2Vx az ax az ду || ||

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Q: Are the partial derivatives and gradients of a function the same, no matter your starting position?

A: Topic:- application of derivatives

Q: Find both first partial derivatives. 5xVy %3D az az ду

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Q: Suppose that your best friend has calculated the partial derivatives of a given functionf(x,y)and…

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Q: use the limit defmition of partial derivative to compute the partial derivatives of the functions at…

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Q: Find partial derivatives of the first and second orders

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Q: How are second-order partial derivatives used in findingextrema?

A: We have to tell how we can find extrema using second-order partial derivatives   The second…

Q: Find the optimum point of this given function using Gradient Descent method and show the error (2…

A: Note:- In this problem you mentioned  to perform 2 iteration. So, the solution is given on the basis…

Q: Maximize 4x+ 2 y+ 2 z

A: We have to maximize f(x,y,z)=4x+2y+2z on the sphere x2+y2+z2=19.Take g(x,y,z)= x2+y2+z2-19=0Thus,…

Q: List the critical points of the function f(x, y) = (x − 1)³(y + 2)² for which the Second Partial…

A: Given fx,y=x-13y+22   To Find: The critical points of the above function for which the Second…

Q: Find the equation for the perpendicular trajectories of the family. 1. x - curve

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Q: Find the second order partial derivatives of f(x.y)-(3x+2y)*4* O Option 4 Option 2 ) Option Option 3

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Q: Find the indicated partial derivative. f(x, y) = x3y9;    fx(5, −1) fx(5, −1) =

A: Partial differentiation of a function with respect to a specified variable can be evaluated by…

Q: 4+2x If g(x.y) = By then the mixed partial derivative at the point (- 2. is:

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Q: Identify all local extrema and saddle points of f(x.y) = 80x + 80y - x - y %3|

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Q: y² + y²eG)° + 2x²•G° x': 2xye 6) Zaye*

A: The solution is given as

Q: invented

A: We have to give the example according to the given information

Q: How do you remember the methods for partial derivatives in the chain rule for several variables?

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Q: In substituting the point (4,1,2) in the partial derivatives, why does the terms without x and y…

A: In part (2), we have the following: ∂g∂x4,1,2=-π1 sin4π -14-1 ln3log332 Now, sin4π=0 So,…

Q: Under what condition does the Second Partials Test fail?

A: Let us consider a function in two variables given as The second partial test for such functions is…

Q: For the points given (1, 5), (2, 7), (3, 6), (4, 10) use partial derivatives to obtain the formula…

A: Given set of data is         1, 5, 2, 7, 3, 6, 4, 10 Use least-square fit              y=ax+b Where…

Q: 5xy = 4x²z – 3yz²; yx and yz.

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Q: Determine the minimum point of fx) =x,²+x,x, +x,² – 3x, – 3x, by using conjugate gradient method,…

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Q: Find both first partial derivatives. z = 14y²Vx az ax az ду eBook

A: We have to find

Q: Use the Chain Rule to compute the partial derivative. би +о In (3u? + uv) = 3u + uv

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Q: Compute the partial derivative In(x² + xy).

A: ∂ ∂ xlnx2+xyTreat y as a constantApply chain Rule,∂ ∂ xlnx2+xy=1x2+xy∂ ∂ xx2+xy                    (…

Q: If the derivative of an analytic function f is 0, does that mean that the partial derivative of f…

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Q: If g(x.y) -4+2x %3D then the mixed partial derivative at the point (- 2. is: 8y

A: we have given g(x, y).  We have to find the mixed partial derivative at the point (-2, 1/2)

Q: Find both first partial derivatives. z = 3xVy az ax az ду || ||

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Q: if f(x,y) = (3^x)(y^8), evaluate the partial derivatives: fx (3,5) = fy (3,5) =

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Q: If f is a function of three variables that has continuous second-order partial derivatives, then…

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Q: evaluate using partial functions *IntegralSymbol* x^5+x-1 / (x^3+1) dx

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Q: Find the perpendicular trajectories of the family of y = ax" curves. N= -1, n=1 and Draw each curve…

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Q: Find the value of at the point (1, 3, 1) if the equation 6xz + ylnx – 5x² – 1 = 0 defines x as a…

A: Given equation is, where x is a function of two independent variables y and z and the partial…

Q: Find both first partial derivatives. z = In() az дх az ду ||

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Q: Find the partial derivative of the following                     y = 3x2z + xz3 – 3z/x2

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Q: Early in the twentieth century, an intelligence test called the Stanford-Binet Test (more commonly…

A: Given: I.Q=MC×100 Find the derivative with respect to M I.QM=1C×100=100C At point (12,10)…

Q: Compute the indicated partial derivative. g(x, у) %3 сos(x + ) 9xxy

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Q: Find both first partial derivatives in) z = az az ду

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Q: Consider a firm whose revenue is expressed through the function R(x,y)= 4x³y², where x and y…

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Q: Find the critical points of the function by using algebraic techniques (completing the square) or by…

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Q: az (8) Find variables z and y and partial derivative exists. if the equation yz – In z = x² +y?…

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