Q.1 The natural domain of function f(x, y) = Inx² + Iny is а) {(х, у):х > 0, у > 0} b) {(х, у):х + 0, у > 0} c) {(x,y): x > 0, y > 0} d) {(x, y): x > 0, y + 0}

Q: 2. Find a function f(r, y, 2) which makes (yz?, rz?, f(r, y, z)) conservative. Show that your answer…

A:

Q: 8, find the the function maximum value of +(x, y,Z) 2179`x+ 2y -12+7 subJect to Constrain t+3 +2² =…

A:

Q: Suppose that f(x, y) = x² + y° at which 0 < x, y and 1x + 8y < 7. 1. Absolute minimum of f(x, y) is…

A:

Q: xyz 3. If f(x, y,z)= In| +e 2 find f,, f, and f..

A:

Q: Determine two functions, defined on the interval (−∞,∞)(−∞,∞), whose Wronskian is given by…

A:

Q: A function (f) is homogeneous of degree • if and only if : ôf + y = Af (x, y). Does the function…

A:

Q: 23:- Find and sketch the domain of the following equations:- 1) f(x,y) = Ln(1 – x² – y²) (2)f(x, y)…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 21. Find div(F), where F(x, y, z) = xyzªi+x²zªj +4x²yz³k. a) -4xyz³+xz4 b) x²y+xz4 c) yz + 3x²yz² d)…

A: Topic = Algebra Correct option = d

Q: Examine for minimum and maximum values of f(x,y,z)=2xyz-4xz-2yz+x^2+y^2+z^2-2x-4y+4z

A:

Q: 2. Find a function f(x, y) which is NOT linear in either a or y and for which the tangent plane at…

A:

Q: 11. Find the linear approximation to given function at indicated point (Баллов: 2) x2 z = 3 + +, Po…

A: Topic:- linear approximation

Q: 4. a) Find an approximation for f (x, y) = at the point (1.97,1.02). V10-r-5y b) Check Euler's…

A: (a) Approximate f(x,y)=410-x2-5y2 at the point (1.97,1.02) (b) Check Euler Theorem for…

Q: 교꾸가고 (a, y) + (0,0) (x, y) = (0,0) f(x, y) = x2+y2 is discontinuous at (0,0).

A:

Q: The function y== In (3z - 2) satisfies the IVP: (3z – 2)°y" + 9 = 0, y(1) = 0, y'(1) = 8. Select one…

A:

Q: Let f (x,y) =In Then f „(1, – 1) =... 3x²+ 4y3

A: This is a problem of partial.

Q: express the extreme value theorem for functions of two variables . find the absolute maximum and…

A:

Q: Use the linearization L(3,-2) (x, y) of f(x, y) = -x²y-xy² near the point (3, -2) to approximate the…

A:

Q: 13 Find the linearizatian z=L(x.y) f the function 2=f(x.y) =4x²-y²42y at the point (x.y) = (3,2).…

A:

Q: 2 3 tegral of the function xy d by x = 0, y = 0, z = C %3D %3D (2(5)

A:

Q: 3) Evaluate elz+y)/(z-y) dA where Ris the quadrilateral with vertices (0,1), (0,-2), (1,0), and…

A:

Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

A:

Q: Find the maximum value of  f(x,y)=3xy(5−10x−5y) over the triangle with vertices (0,0), (1/2,0) and…

A: Given :            f(x, y)= 3xy(5-10x-5y)            Vertices (0, 0) (1/2, 0) and (0, 1)

Q: (xy(x²–y²) f(x, y) = { (x²+y²) (x, y) # (0,0) (x, y) = (0,0) ) show that fxy(0,0) f yx(0,0) Let

A:

Q: Find a point zo where the function f (z) = (z – 8 – 10i) (z – 8 – 10i) is differentiable. What is…

A:

Q: What does it mean for the differentiability of a function if only one of the Cauchy-Reimann…

A:

Q: 2² – 6y? Then Let f(x, y, z) y2 + 4z² fz(x,y, z)= fy(x, y, z)= f-(x, Y, z)=

A:

Q: Suppose that f(x, y) = x² + y² at which 0 < x, y and 4x + 7y < 9. 1. Absolute minimum of f(x, y) is…

A:

Q: What does it mean for the differentiability of a function if the Cauchy-Reimann equations (Ux = Vy…

A:

Q: 2.2 11, IfF = xyz\+x*y°z}+ xyz k then find div F at (2, 1, – 3).

A:

Q: The function f(z) 2x-36z+120z-8 has two critical numbers. The smaller one is x = and the larger one…

A: A critical point is a point in the domain of the function where the function is either not…

Q: what is the global maximum and minimum of: f(x,y) = y^2 +xy -xy^2   in (0≤ x ≤ 1) and (1≤ y ≤ 2)

A:

Q: Let f(x, y, z)= = fz(x, y, z)= fy(x, y, z)= fz(x, y, z)= 2² - 2y² I y² + 4z² Then

A:

Q: The shaded region is a domain for the function eq1 eq2 -1 -1 A) ƒ(x, y) = V4 – x² – y² + Vx – y² +…

A:

Q: 7) Let Z.= 3x2 - y² . Find all points at which |VZ| = 6 %3D

A: There is an ellipse,  all points on the ellipse are the solutions of given equation.

Q: 1. Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1,2).

A: Given triangular region is bound by the vertices 0,0, 1,0 and 1,2. The sides of the given triangular…

Q: 3,4 Find the maximum of the Xy z°t* when all the variables X, y, Z and t are all positive and…

A: We have to find out the maximum value ofxy2z3t4

Q: 5. Find and sketch the domain of the functions (3D) A) f(x, y, z)=√√√1-x² - y²z² B) f(x, y, z) =…

A:

Q: Suppose that f(x, y, z) = 4x + 4y + 3z at which 0 < x, y, z < 5. 1. Absolute minimum of f(x, y, z)…

A: We have to find the absolute minima and maxima.

Q: 1 3. Let f(x, y, z) = Show that Vx2 + y² + z²° frx + fyy + fz2 = 0.

A: Given fx,y,z=1x2+y2+z2 To show fxx,+fyy+ fzz=0

Q: Suppose that f(x, y) = x² + y at which 0 < x, y and 3x + 9y < 7. 1. Absolute minimum of f(x, y) is…

A:

Q: the absolute maximum and minimum values of f(x,y)= x²-2xy+2y on the rectangle defined I in the…

A:

Q: 2 f(x, y) = x² + 3xy

A:

Q: 4. For the function f(x, y) = exp (ax + by) find the maximal possible value of the directional…

A: In this question we will use basic of calculus i.e concept of vector calculus. We will find the…

Q: 1. Show that the function x2 – y2 2xy f(x,y) ={ x2 + y? if (x,y) # 0 if (x, y) = 0 is continuous at…

A: If for every ε&gt;0, there exists a δ&gt;0, such that if |x-a|&lt;δ, |y-a|&lt;δ, then the function…

Q: Find and sketch the domain of the function. f(x, y, z) = ln(64 − 4x2 − 16y2 − z2)

A: Given function is      f(x,y,z) = ln(64-4x2-16y2-z2) We have to find the domain of this function.

Q: 5. Assume that the following conditions exist fi = 0 2= 0 Does a maximum, minimum, or saddle point…

A:

Q: Q3: Find fxx of the function f (x, y, z) = -In/1-x2 - y2 – z2 %3D

A:

Q: 1. How do you find the linearization of f(x) at x = a? Illustrate with a concrete example

A: We have to solve

Q: (b) Show that the function defined by xy √√√²+y² f(x, y) 0 if (x, y) = (0,0) is not differentiable…

A: We have to show that the function defined by…