2. T1: R2 - R2, T1(x, y) = (x – 2y, 5x + 2y) T2: R2 - R2, T2(x, y) = (0, x)

Q: Find the values of x, y, z at which f (x, y, z) = x2 + 4y2 + 5z2 - 6x + 8y + 3 assumes its minimum…

A: f(x, y, z)=x2+4y2+5z2-6x+8y+3   we have to find all points of x, y, z Taking, ∂f∂x=0, ∂f∂y=0 and…

Q: A miniature quadcopter flies in a curve line from one point to another. Suppose that the path of the…

A: We have to find arc length L= ∫ab1+dydx2dx

Q: = x2 - 4x + 1 with domain [0, 3] f has ---Select--- v at (x, y) = f has ---Select--- v at (x, y) = f…

A:

Q: Find the point on the planez = x + y + 1closest to the point P = (1, 0, 0). Hint: Minimize the…

A: Let Q(x,y,z) be the point closest to the point P. Let D be the distance between these two points.…

Q: A miniature quadcopter flies in a curve line from one point to another. Suppose that the path of the…

A: The function that depicts the path of quadcopter is as follows:…

Q: Find the point where the maximum value of f(x, y) = xy subject to y = 33 – x² occurs. (x, y, z) =

A: (x,y,z) = (√11,  22,  22√11)  The detailed solution is as follows below:

Q: f(x,y)=x² +16xy + y² +8

A:

Q: Let f(x, y) = 3x² – x – 3y + 5y2 – 10xy. - - - List the critical point:

A:

Q: Expand x'y + 3y - 4 about the point (1, -2) by Taylor' s theorem.

A: Let, the given function be fx,y=x2y+3y-4 and the given point is 1,-2

Q: A miniature quadcopter flies in a curve line from one point to another. Suppose that the path of the…

A: The function that depicts the path of quadcopter is as follows:…

Q: Find the four second partial derivatives. z = 7x2 + y9 ax? azz дхду дудх az ay? %3D II II II

A: We have to find the four second partial derivative of the given function. The given function is…

Q: Q4/ Linearize the Function Z = XY2 About X, = 3, Y, = 6 using: a) Absolute Variables b) Perturbation…

A:

Q: If f(x, y, z) = 12ry - 2yz - 6zx + 7, then the first order partial derivative f = O - (2y – 6x) (2y…

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: Vx2 +1 – Vx² – 1 y = Vx² +1+ vx² – 1 2.x3 dy = 2x - d.x - - show that Vx4 – 1 -

A: Given: y=x2+1-x2-1x2+1+x2-1      ......(1) To Prove:  dydx=2x-2x3x4-1      ......(2)

Q: Find the orthogonal trajectories of x² + y² – 2cy = 0

A:

Q: F(1), p(y) - y - 1, F(Y) - F(y - 1), y - 2, 3, ...

A: Suppose that Y is random variable that takes on only integer value 1,2,.. and has distribution…

Q: g(x, y) = 6x² – 3y², (/8, /5) Gradient is f(r, y) = tan 6y (16, 2) Gradient is

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: Find the maximum value that f(x, y, z) = x² + 8y - z² can have on the line of intersection of the…

A: Given function is f(x,y,z)=x2+8y-z2 and the other constraints are g(x,y,z)=2x-yh(x,y,z)=y+3z We…

Q: +[2yln [2yin (3 3y²dx 3siny dy = 0 ;when x = 1, y = 0 5x x2+3x x+3,

A:

Q: 2. y = V4-x , x=0 and y=0 about the y- axis

A: Given that y=4-x2, x=0 and y=0 about the y-axis

Q: Determine D,f(3,-1,0)for f(xy.z) = 4x-y'e in the direction of i = (-1,4,2, (Express your final…

A:

Q: Compute the partial derivative fa(, 4, 2) of the function f(2,4, 2) = yz' + 2 – 2 vy + * +2 y. O…

A:

Q: y" + 4y' + 3y = 0, y(0) = 2, y(0) = -1

A:

Q: Find both first partial derivatives. z=(4 xy)/(x^2+y^2) fx(x,y)= fy(x,y)=

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: 3. x - y=t + 3 4. x = VT-T; y =t- 3t 5. x = vE + 2; y = t² - 3

A:

Q: 4) Find all first-order partial derivatives w = f(x,y, z) = 2x³y³ – /xyz + 4z6x y3

A:

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: From the given information the given curves from which the volume is to be generated are:

Q: Find both first partial derivatives. f(x, у) %3D 3х — 8y + 4 fx(X, y) fy(x, y)

A:

Q: C(x, y, z) = 90 + 6x + 4y + z where x is the cost of 1 pound of one raw material, y is the cost of 1…

A:

Q: x² + y² = (2x² + 2y² – x)', (0,¿), (cardioid) -

A:

Q: Obtain the particular solution for: 2y" +2y=2sinx y(0)=0, y'(0) =1 By using method of variation…

A:

Q: : Find fz for f(x, y, z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

A:

Q: (3z²+5z+3)dz (z- 2)(z+3) Integrate:

A: The given integral is ∫(3x2+5x+3)(x-2)(x+3)2dx

Q: Find the maximum and minimum value of f (x,y) =x' + 3xy² – 3x² – 3y² +4 = X" - -

A:

Q: A miniature quadcopter flies in a curve line from one point to another. Suppose that the path of the…

A: The given path as y=fx is y=2.15+2.09x−0.41x2 for 0≤x≤3.6. The arc length is calculated by…

Q: 3z2+x 30. If z – xz – y = 0, prove that- =- ax dy (3z²–x)³*

A: Let's find.

Q: y" + 3y' = 0, y(0) = -2, y'(0) = 3

A: The solution is given as

Q: (2)If ø = xyz – 2 y²z+x²z?. Find div grad ø at points (2,4,1)

A: Given that        Φ =xyz-2y2z+x2z2  Here we have to find div grad Φ at points (2,4,1).

Q: Classify the critical point (5,-4) for f(x,y) = x² + 4xy + 2y2 + 6x-4y +3

A:

Q: 1 y" – 2y' + 2y y(4) = 0, 3 (4) = 0. -

A: Given: The given differential equation is y''-2y'+2y=1x, y4=0,y'4=0

Q: Find fz for f(x, y, z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Integrate f(x,y, z) = 2x – 3y² – 2z+3 over the line segment from the origin to (1, 1, 1) and over…

A: A parametric curve is a normal curve where we choose to define the curve`s x and y values in terms…

Q: dN1 =rN1 dt (1-*) - aN1 N2(1 – exp[-bN1]), K %3D dN2 = -dN2+ N2e(1 – exp[-bN1]), dt

A:

Q: Show that the function f(x, y) = 3x - 4y² is differentiable at point (−1, 2)

A: answer is in next step. please give a like !!!

Q: (b) Form the partial equation by eliminating function f from z = f(x?

A:

Q: Calculate fz(2, 3, 1), where f(x, y, z) = xyz.

A: Given,          fx,y,z=xyz

Q: I Sdve for dydx using the four-step rule 2. Y = x- x 2.

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.