The average amount of time that a customer waits in line for service is given by w(x, y) = 1/x−y where y is the average arrival rate and x is the average service wait measured in the number of customers per hour. (A) Find the domain of w. (B) Find w(10,9).

Q: Find all values of x such that dy/ldx = 0 where y is the function stated below. x2 y = -3x + 4)

A:

Q: Find absolute maxima and minima of the function f(x; y) = x^2 + y^2 on the closed triangular plate…

A: The points are:

Q: 2. Find the derivative of the function at PO in the direction of u. f(x,y)=6x-7y, P0(-7,-2), u=4i-3j

A: We have to find derivative

Q: find the orthogonal trajectories of the family of curves x2+y2=a2

A:

Q: The function f (x, y) = 2x + 3y + 9 - x2 - xy - y2 has a maximum at some point (x, y). Find the…

A:

Q: 4xy* :- find f,,f, at point (4,1) for f(x,y) = x’e**Y

A: I have used partial differentiation

Q: Suppose a person wants to travel D miles at a constant speed of (30 + x) mi/hr, where x could be…

A:

Q: Find the orthogonal trajectories to the family of curves: x² = C-v'(ln y² –1).

A:

Q: Find y' for y = vTy at the point (9,1).

A: Given: y=xy ⇒y=x12y12 ⇒y12=x12

Q: Given f (x,y) = x³ + y3 – 3y² – 3x² – 9y, find the critical points and use the Second Derivative…

A: solution :-

Q: Find f, fy. f- f(x.y.z) = 3x - 4y 2. 2 +z?

A:

Q: A:- Find the orthogonal trajectories for functions In -1) = - COS X +a y

A: The given family of curves is: lny-1y=-cos x+a ,            where a is an arbitrary constant.

Q: Use the second-derivative test to show that the function f(x, y) = x²eY – y²e* has a saddle point at…

A: A point (a,b) of function f(x,y) is said to be the saddle point if it is a critical point…

Q: 3. Find the derivative of the function f(x, y, z) = xy³ + yz³ + zx³ at the point (-1, 2, 1) in the…

A:

Q: Find the orthogonal trajectories of the functiony x + ce which is passing through (-2,0)

A:

Q: Use variation of parameters to find a particular solution of the ODE y" – y = 2e".

A: Given differential equation is  y''-y=2ex we have to find  the particular solution of this…

Q: For function f(x, y) = 5- | 2 E find the maximum value of the directional derivative at (3, 2).

A:

Q: Find the absolute maximum and minimum of the function on the given domain. f(x.y) = 6x + 5y on the…

A:

Q: Find the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to…

A: The solution is given as

Q: Find a slope of the solution of y' = t – y at (3,1).

A: We have been given a linear differential equation dydt=t−y ______(i) (As y′=dydt)We have to find the…

Q: b. Find the orthogonal trajectories for the family of curves x² + y² =C².

A: we have to find the orthogonal trajectory of the given family of curve

Q: Find the maximum rate of change of the function f(x,y) =4x^2-2y^3 at the point (1,1)

A: Given data: The given function is f(x,y)=4x2-2y3. The given point is (a, b)=(1, 1). The expression…

Q: Find the critical points of the function f(x,y)=x^(4) + y^(4) − 144xy

A:

Q: Find the gradient of the function y = x³ + x² – 2x at points where - a. It crosses the x -axis b. It…

A:

Q: Find the absolute maximum and minimum of the function f(x,y) = 2x² - 4x + y² - 4y +6 on the closed…

A: Given that a function f( x , y ) =2x2-4x+y2-4y+6  on the closed triangular plate bounded by the…

Q: (5) Find the curve y = f(x) in the xy-plane that passes through the point (9, 4) and whose slope at…

A:

Q: Q2 (a) A miniature quadcopter flies in a curve line from one point to another. Suppose that the path…

A:

Q: Find the maximum slope on the graph of f(x, y) = 4 sin(xy) at the point P(5, 0). 1. max slope 20T 2.…

A: Given:- f(x, y) = 4 sin(xy) To find:- Find the maximum slope on the graph of f(x, y) = 4 sin(xy) at…

Q: Q2 (a) A miniature quadcopter flies in a curve line from one point to another. Suppose that the path…

A:

Q: f (x, y) = 3x^3 −9x+9xy^2. Use the second derivative test to classify the critical point (1,0) as a…

A: Recall: second derivative test : (i)  Firstly find critical points . i.e, fx(x,y) =0 and…

Q: Suppose that f(x, y) = e¯4z² - ly + 7z + 2y then find the discriminant of f.

A:

Q: Q, Frd the donain of H fallowing function: fa) = 5x -3x-4

A:

Q: Find the orthogonal trajectories of x^2+y^2−2cy=0

A:

Q: Find the linear approximation of f(x) = Vx-1 approximate 2.02. near a = 2. Use the result to

A:

Q: x² – y² = = CX

A: For orthogonal trajectories, replace dy/dx by -dx/dy and solve it.

Q: Find the linear approximation of the function y = x' at point xo 1 О а. у %3D Зх — 2 -

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: We have to solve

Q: Find the absolute maximum and minimum of the function f(x,y) = 2x - 8x + y - 8y + 2 on the closed…

A:

Q: Find absolute maxima and minima of the function f(x;y) = x^2 +y^2 on the closed triangular plate…

A:

Q: Find the orthogonal trajectories of the family of curves x2+y2=a2

A: We have to find the orthogonal trajectories of the family of curves x2+y2=a2.

Q: Find f fy. - f(x.y.z) = x - Vy² + 22? + 2z² = (Type an exact answer using

A: Here we have to find fx , fy and fz  of

Q: Find the maximum slope on the graph of f(x, y) = 2 sin(ry) at the point P(4, 0).

A: The given question can be solved as shown in step2.

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: Found the line of differentiability of f(z)=x2 - 2xy + 3y + i(2xy - y2 +x)

A: Answer

Q: Find the linearization of the function f(x)=x2+2cosx at a=0.

A: Linearization of a function f(x) at x = a is given by, Now,

Q: Find the linearization of the function z =/ at the point (-5, 1). L(1, y)

A:

Q: 4. What is the direction in which the function f(x, y) = yx² -- decreases most rapidly at the point…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the direction at which the function f (x, у, 2) %3 хIn(е' — хг) increases fastest at (-3,0,0)

A:

Q: Find a function f:R² → R, its tangent plane at the point (1; 1; f(1; 1)) is given by -2x – 9y – z+8…

A: