Consider the function h(x, y, z) = x² - 2y² + 3z², = and its level surface S through the point (1, 1, 1). Determine the shortest distance from S to the origin by considering the function f(x, y, z) x² + y² + z² and writing down the Lagrangian for finding the minimum of f subject to (x, y, z) lying on S. Determine the critical points and by comparison of the values of fat these points determine the minimum distance.

Q: BA)Find normal line and parallel plane to the function f(x, y, z)=x√yz + 6 At point (-3,1,4).

A:

Q: Find the maximum value of ƒ(x, y) = x²y6 for x, y ≥ 0 on the unit circle. fmax =

A:

Q: Sara draws the 4 of hearts from a standard deck of 52 cards. Without replacing the first card, she…

A: Given, Sara draws the 4 of hearts from a standard deck of 52 cards without replacing. a) we know…

Q: Classify all level curves of f(x, y) = Vy² – x² and draw its contour map.

A:

Q: Let f(x.y) = ry. a. Sketch/describe the domain of g Domain = { (x,y)]yz0} b. Sketch a contour map…

A:

Q: Question 2 Find the minimum value of (x.y)=2xr+4y on the curve x^2+xy+y^2=16 Select one: а. -18 C b.…

A: Given, fx,y=2x+4yx2+xy+y2=16         let gx, ygx,y=x2+xy+y2-16

Q: Consider the function f(x, y) = 2x²-3xy + 8y² + 2x - 4y +4 at the point P(-2,1). a) Find a vector…

A: Let  be a function, thena) the gradient  gives the direction of the steepest ascent at point…

Q: n exact form. Use symbolic notation and fractions where needed.)

A:

Q: For the function f(x,y) = 100 - x^2 - y^2 a) Draw the cross-section of f(x,y) with x fixed at x =…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: -3. 3) to the curve given by f(x) =

A:

Q: 5 уx(1-3 ху) )= 1+xy el punto (1,8) y úsela para estimar f(1.2,8.2).

A:

Q: Q3A) Find normal line and parallel plane to the function f(x, y, z) = x²y²z² - 4 At point (1,-1,2).

A:

Q: =

A:

Q: Which point on the curve y = Vx – 1 + 8 is closest to the point (5, 8)? (x, V) = ( What is this…

A:

Q: 3 Find the Minimum distance from the origin to the plane X+2y-z=5

A:

Q: Find the points on the graph of the function f(x) = x^2 that are closest to (0, 2) in the xy-plane.…

A: Minimal distance

Q: Suppose that z is an implicit function of x and y in a neighborhood of the point P = (0, −3, 1) of…

A: Equation of a line passing through point (a, b, c) and parallel to vector <p, q, r> can be…

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx2 + y2 + z² (7,…

A:

Q: Sketch a typical level surface for the function f(x,y,z) = 3x² + 3y² + 3z².

A: Given that the function is                       f(x, y, z)=3x2+3y2+3z2.

Q: Sketch the level curve of f(x, y) = x² — y² that passes through 5) : P = (–2, − 1) and draw the…

A: