Q2// A :- find and sketch the Domain of f(x, y)=v(x-4)+y' -9 + V4-x²-y° 2

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 linearization of the function f(x,y) = ln(x3y6) at the point (x0,y0) = (4, 3). Leave all…

A: Given fx,y=lnx3y6     at (4, 3) The linear approximation in 2 variables is given by Lx, y=fa,…

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

A:

Q: A heat-seeking particle is located at the point (2, 3) on a flat metal plate whose temperature at a…

A:

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

A: I have used partial differentiation

Q: Find the linearization at x = a. IT f(x) = sin³ (x), a = 4

A: Given,            The linearization at x=a.             fx=sin3x, a=π4We know that,             The…

Q: Suppose F(r, y) is a C' function such that F(0, 0) = 0. What conditions on F will guarantee that the…

A: Let us consider, F^(x,y)=F(F(x,y),y)  On applying the implicit function theorem , can get a solution…

Q: Express in form y=f(x) by eleminating the parameter x = t + 3, y = 4t

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: Tangent to the curve z2 = 2xy + x2 , z = 3 , at the point ( 1, 4, 3) %3|

A: For a surface of the form: f(x, y, z)=0, the equation of the tangent at x0, y0, z0 is defined as…

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: Q4) Find y" + 3y' 5y at x-5 where y = xsin(1/escx))

A: To find the y"+3y'×5y at x=5  Given y=xsin(1/cscx)

Q: (6) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

A: Orthogonal trajectory curve of a family of curve is defined as a curve which intersects every member…

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: Find the linearization of the function a) z = cos(sin y – x); at (-2,0) and use it to approximate…

A: Suppose f(x,y) be a differentiable function at (a,b). Then linearization of f(x,y) at (a,b) is given…

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

A:

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

A:

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

A:

Q: 3. Given the function f(x, y, z) = In(x² + y² – 42²), find the directional derivative f, in the…

A:

Q: The temperature in degrees centigrade (◦C) at each point (x, y) on a curve 2x + y = 3 is given by…

A: For relative maximum or minimum To maximize or minimize  a function f(x) 1st we need to find its…

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: Determine the coefficients a, b, c, and d, so that the curve y = ax' + bx² + cx + d have critical…

A: Since you have asked multiple questions, as per our policy we will answer first question. Please…

Q: Find the linearization of f (x, y)= e²"¬*, at (0, 7 / 2).

A:

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

A:

Q: A rectangular plate with an area of 36 cm? is to be produced on a lathe in such a way that the…

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

A:

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

A:

Q: Let f(x,y)= 3+cos(x) sin(2y) a) Show that the function has a stationary point at (0,Pi/4). b) Is (0,…

A: To analyze the critical point (0,pi/4) of the given function of two variables

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 ∇f at the given point. ƒ(x, y, z) = x2 + y2 - 2z2 + z ln x, (1, 1, 1)

A: Given function is fx,y,z=x2+y2-2z2+zlnx and point=1,1,1

Q: 4. Determine the constant a,b, c, and d so that the curve defined by f(x) = ax³ + bx² + cx + d has a…

A:

Q: A heat-seeking particle is located at the point (2, −2) on a metal plate whose temperature at (x,y)…

A:

Q: V Solve usıng variaton of parameters or reduction of order (D²+1) y = tan

A:

Q: 2 f(x, y) = x² + 3xy

A:

Q: Determine the linearization of y = 4 – 2x at (1, 2). Then use it to approximate the value of y when…

A: It is given that, y=4-2x2  at 1,2 we have to determine the linearization of function. Then use it to…

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

A:

Q: What is dufferential equation of x'=4x-y and y'=-4x+4y when t=0, x(0)=1 and y(0)=1

A:

Q: Tangent to the curve z2 = 2xy + x² , z = 3 , at the point ( 1, 4 , 3

A:

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: (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…

Q: (6) Find the orthogonal trajectories of the family of curves r= 2C sin 0, where C being parameter.

A: See the detailed solution below.