Q4: Find and classify the extreme points of f (x, y) = 3x?y+y3 - 3x2 – 3y2 +2.

Q: Find the extrema of f(x,y) = xy + 14 subject to  x2 + y2 = 18.

A: To Determine: Find the extrema of f(x,y) = xy + 14 subject to                         x2 + y2 = 18.…

Q: Find all the points of g(x, y) = x³ − 3x + 3xy² where a relative extrema might occur.

A:

Q: Find and classify the critical points of f(x,y) = 2 – x +2a2 - y². %3D

A:

Q: Find the maximum value of f(x, y) = 4x + 6y subject to being on the circle ² +y² = 13.

A: We use formula of Lagrange's multiple Del(f(x)) = lamda * del(g(x))

Q: f(x) = Vxdx 0. 1. Trapezoidal Rule

A:

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A:

Q: For the function ex, the linear approximation around x = 2 is %3D

A: Introduction :

Q: Find the length of the curve y 2ln(x) from x 1 to x =4. %3D

A:

Q: Find and classify the critical points of f(x, y) = 6xy – 4x³ – 3y?

A: According to our guidelines, we can answer only one question or three subparts of a question. other…

Q: *z + yz? + 2ry? - = 0 ve z = f (x, y) ise =? what is the f(0,1) at

A:

Q: Suppose that f(z, y) – e ¯4r² - 4y² - z + 2y Then the maximum is

A: The given function is: f(x,y)=e-4x2-4y2-x+2y Here,…

Q: Q1 Find thr relative maximum and minimum of: fx, y) = x² + y² + z?given that 9x? + 4 y² + 2z? = 36…

A: Consider the provided question,  minimize and maximize, fx,y,z=x2+y2+z2                        ....1…

Q: 3. Describe the level surfaces of the function. f(x, y, 2) = x² + 4y? + 42?

A: We Know that,  A level surface of a function w = f(x, y, z) with three variables is a surface f(x,…

Q: Q2: A-The Trapezoidal rule for roodx 5 and Midpoint rule /)dx=4 What value does . Simpsons rule give…

A: 1st we will find relation between trapizoidal , mid point and simpson rule . Then will use this…

Q: 2. For what value of k will x – iky F(x, y) = (x+ y)² + be analytic?

A: Given function is fx,y=x+y2+x-ikyx+iy If it is analytic then it satisfy C-R equation ux=vyuy=-vx

Q: Find the maximum and minimum values of f(x, y) = x² + 2y² on the quarter circle x² + y² ≤ 4 with r,…

A:

Q: Find the relative maximum and minimum values. f(x,y) = 3x² – 4y?

A:

Q: Show that the function (x2+y2 t224이) is a Solution of Loplace's equation d2u dy?

A: It will be solution of given Laplace equation only when, it will satisfy it.

Q: dz dz and of the function xsin(y+ z) – xy + z² = 2y. ду -. Find the əx

A:

Q: Q2: Find all relative extrema and saddle point of f(x,y) = 3xy +y-x' +3

A:

Q: 1. a- Find a result by using variable separation for ý=secy h- xy = x + y

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: Find the Maximum value of the function f(x, y) = x² – y² – 2y on the curve x? + y? = 25. %3D -

A: By langrange multiplier method n

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: 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: Find the particular sölution f"(x) = 4, f'(2) = 12, f(2) = 17

A: integration 2 times and after applying initial condition we get f(x)

Q: Picture attached. Thanks in advance!

A:

Q: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

A:

Q: Find all points (x,y) where f(x,y) has a possible relative maximum or minimum. f(x,y) = x4 - 4xy +…

A:

Q: Find the orthogonal trajectories of the family of curves x² + Y? = R? %3D

A:

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

A:

Q: Find the point on the graph of z = x2 + y2 + 10 nearest the plane x + 2y - z = 0.

A:

Q: Find a simple closed curve C with counterclockwise orien- tation that maximizes the value of f t* dx…

A: Given an integral. We need to find the C that maximises the value of the integration.  Let's start.

Q: find the points on the curve x^2+xy+y^2=16 which one nearest and farthest from the origin using…

A: Let us consider the given function f(x,y) Subjected to g(x,y)=C Solving using Lagrange's multipliers…

Q: Q4/ Find the length of the curve y () (x² + 2) from x 0 to x= 3.

A: The length of a curve f(x) on an interval [a,b] is: L=∫ab1+(f'(x))2dx Where f'(x) is the first…

Q: ) Let Z = 3x2 – y². Find all points at which |VZ| = 6

A: Since you have asked multiple questions in a single request, we would be answering only the first…

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

A:

Q: Q.2/ Test the following surfaces for maxima, minima and saddle point:- Z(x.y) = xy + 7x – 12y°x² –…

A: Given, Surface is Z(x,y)=xy+7x2-12y2x2-6x+5 If rt-s2>0 and r>0 then the function has minimum…

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

A:

Q: 5 B) Find y" for the function y = x + Vx at p(1,3)

A: Given query is to find the double derivative of the expression at point p.

Q: Compute the length of the curve: f (x) = x² 2x, 0<x<2

A: Given:- f(x) =x2 -2x  To find:-  Length of curve over interval [0, 2]

Q: Q3/ Optimize the function Z = x + xị ? Subject to: x1 + x2 = 4 11,x2, 2 0 Using Lagrange…

A:

Q: 3 Q1// :- find fy,fy at point (4,1) for f(x,y) = Xe

A:

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: 2) Find the relative maximum or minimum value of f(x, y) = 3x² + 2xy + 10y² - 54x - 308y

A:

Q: At what x-value(s) on the interval [-2, 3] does the graph of f (x) = x² + 2x – 1 satisfy the M.V.T.?

A: According to mean value theorem,Let f be continuous on [a,b] anddifferentiable on (a,b). Then…

Q: Check whether z/z+3 is analytic or not by C-R equation?

A:

Q: Find the local extremum of the function • f(x,y) = xy² – 6x² – 3y²

A: Find the local extremum of the function f(x,y) = xy2 - 6x2 - 3y2