af , Given the function f (x,y) = 3x – x²y² + 2x°y, what is iTe ду А. 3 — 2ху? + бх?у В. - 2х3у + 2x3 C. 3 – 2xy² + 8x²y D. 3 – 4xy² + 6x²y -

Q: If W[y,, Y2 Y3]=0, then {y1, y2 , y3} must linearly dependent, where y1, y2 , y3 are diffferentiable…

A: To find- If Wy1, y2, y3 = 0, then y1, y2, y3 must linearly dependent, where y1, y2, y3 are…

Q: Suppose that a = x(t) and y = y(t) are both functions of t. If a² + y} = 29, %3D and d = 1 when a =…

A: The given equation is x2+y2=29. Now find the derivative dydt, when x=5, y=2 and dxdt=1as follows.

Q: Find the exact value of Duf(-2,-1,-3) in the direction of v = 3i+ 4j + 5k for the function f(x,y, z)…

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Q: The function f(x, y, z) = x² – y² = z² increases in the direction at the point (1, 1, 1).

A: We need to find if the statement is true or false.

Q: 3. Classify the stationary points of (a) f(r, y, 2)= x² +x*y+y*z+ – 42 (b) /(2, 23, re)- 20xy…

A: a) stationary point of f(x, y, z):-At those points where∂f∂x=0,∂f∂y=0,∂f∂z=0…

Q: Which of the following is the function h(x,y) that satisfies the equation h(x, y).fxx+ X.fxy-fyy =0…

A: We will calculate all the partial derivativea and proceed

Q: The function f(x, y, z) = x² − y² − z ² increases in the direction 〈六〉 (1, 1, 1). at the point

A: Please check step 2 for solution.

Q: Since fy(x, y) = x², find f(x, y). f(x, y) = + g(y)

A:

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

A:

Q: 2. Find a function f(r, y, 2) which makes (yz?, rz?, f(r, y, z)) conservative. Show that your answer…

A:

Q: Q.1B) If w = f(u,v) where u = tan"12 &v=In(x² + y²), the show that: dw Х- +- дх дw dw <-2- ду ду

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Utt = Uxx, x>0, t > 0, u(x,0) = f(x), u₁(x,0) = 0, u₂(0,t) = 0, where f(x) = { b) Sketch the…

A: solutions are given below:

Q: Find the linear approximation to the equation f(x, y) = 3, zy at the point (6,2,6), and use it to…

A:

Q: Determine whether X and Y are independent: 2e--2y x, y > 0 a. fxy(x, y) =

A: Hello! As you have posted 2 different questions, we are answering the first question (4-2). In case…

Q: 6) If F = (3x²y – z)i+ xz3 + y*)j – 2x³z²k, find V(V - F) at the point (2,1,0).

A:

Q: Suppose that f(z, y) = 10z²y² + 8z? + 2y? then find the discriminant of f.

A: We have to find the discriminant of the function of two variables fx, y. It is given that the…

Q: T: R2 R2 is defined by х + 7х, [3x, – 4x2] X1 %3D and B = {u,,u,} and B' = {v,v,}, where %3D -- --…

A: Given transformation T:R2→R2, defined by Tx1x2=x1+7x23x1-4x2 and B=u1, u2 and B'=v1,v2 Here u1=22,…

Q: Find the linear approximation to the equation f(x, y) = 2, at the point (4,2,4), and use it to 2 %3D…

A:

Q: Find the linearization L(x, y) of the function f(x, y) = V161 – læ2 – 16y² at (-4, –3). L(x, y) = ||…

A:

Q: If Wly, , y2. Yal = 0, then (y1, y2 , y3) must linearly dependent, where y1, y2 , y3 are…

A: Given that if  W[y1,y2,y3]=0, then {y1, y2,y3} must linearly dependent, where y1,y2,y3 are…

Q: Solve ux – uy +yu = 0, where u is a function of x and y. %3D

A: Given: ux-uy+yu=0. The objective is to solve u, where u is a function of x and y.

Q: What is the gradient of f(x, y) = x² - y4 at the point (5,2)? O 5i + 16j O -15i-16j O -6i + 13j O…

A:

Q: Find the linearization of the function f(x, y) 155 – 2x2 – 5y² at the point (5, 4). L(x, y) = Use…

A: Given:      f(x,y) = √ (155 - 2x2 - 5y2 )     Point : ( 5 , 4 )  Now     Linear approximation f (…

Q: Let f(x, y, 2) =x² + 3r°y? + 2°, g(u, v) = (u² + v², uv, 3u – 2v). Find the derivative of f(g(u, v))…

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Q: If Wly, Y2 Y3]= 0, then (y1, y2, y3) must linearly dependent, where y1, y2 , y3 are diffferentiable…

A:

Q: Solve Ut = Urx, x > 0, t> 0, u (x, 0) = f (x), u (0, t) = 0.

A: Given partial differential equation isut=uxx,     x&gt;0,     t&gt;0ux, 0=fxu0, t=0

Q: • Find the direction in which f(x,y) = yeY increases most rapidly at the point (0, 2). %3D

A:

Q: Find the gradient of the function w = 2x²y – 4yz + a at the point (1, 1, -2). O 2i+ 10j- 8k O 4i+…

A:

Q: Calculate fw(-1, 2, 0, – 1) where f(x, y, z, w) = xy²z – xu? – e2²-y²–2²+2w=

A: Given that fx,y,z,w=xy2z−xw2−e2x2−y2−z2+2w2 To calculate: fw−1,2,0,−1

Q: In x - direction (+ -) - Fu + P,A,- P3A3 cos 40° m, V, cos 40° - m, V. F = P1A,- P3A, cos 40° + m,…

A: To identify for True or False.

Q: What does it mean for the differentiability of a function if the Cauchy-Reimann equations (Ux = Vy…

A:

Q: function f(x, y) = 2x^3 + 6xy^2 −3y^3 −150x has four stationary points, find

A: Please refer to the image below

Q: If W[y, , y2• Y3]=0, then {y1 , y2 , y3} must linearly dependent, where y1 , y2 , y3 are…

A:

Q: f(x,y)=x^2+9y^2 What is the direction in which f changes most rapidly at point (1,2)?

A:

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: Find the directions in which ƒ(x, y) = (x2/2) + (y2/2) (a) increases most rapidly at the point (1,…

A: We have to find the directions a) Given function is  f(x, y)=x22+y22∆f=∂f∂xi^+∂f∂yj^∆f=122x i^+122y…

Q: f(2ecz tan z - 6z")dz=_ • tan z+z+e secz+z+e • secz-z+e - secz-z+c •- secz+z+e

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: Given f(x, y, z) = /2x – y – 5z, find - - f-(x, Y, z) = %3D f,(x, Y, 2) = %3D f-(x, Y, z) =

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Q: f (x, y) = {* - kx(x — у),0 <x< 2,-х <у<х elsewhere

A: (i) Consider the property for a joint PDF, ∫-∞∞∫-∞∞fx,ydydx=1 Substitute the values,…

Q: (h) be the function of two variables (a) If, in addition, x=r cost and y=r sint, find the value of…

A: 'f' is a function of two variables such that ∇→f(x, y)=3x2-3y, -3x+3y2 f(2, 1)=4

Q: 12. What is the directional derivative of f(r, y, z) = ba?y2² +x² + y? +22 in the direction of (8,…

A: Given that fx,y,z=bx2y2z2+x2+y2+z2 in the direction (8,9,12) find out the directional derivative

Q: If f(x,v) = (y)²x ,Verify fy=fx ху

A: Given:fx,y=y2x Now, the value of fxy will be,fxy=∂2f∂y∂x=∂∂y∂f∂x=∂∂y∂y2x∂x Now, the value of ∂y2x∂x…

Q: 2. Show that the function u = p(ry) + /TY p(y/x) provides the equation ‚Pu dy² y² = 0. %3D

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: Calculate Duf(0,–2,5) in the direction of v = -3i + 12j – 4k for the function f(x,y,z) = 3x² + xy –…

A:

Q: What is the gradient of f(x, y) = x² - y4 at the point (5, 2)? O 5i + 16j O -15i-16j O -6i + 13j O…

A:

Q: f (x, y, 2) = x³ /+42³y² – xyz +x² – Vz5 VI+ 42°y? – ryz+ x² – Vz5 - -

A:

Q: Suppose A = xy" where x, y e R". Show that ||A||2 = ||x||2||y||2-.

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: íf was T'fz (R)→R Linearidentifier grand father ♡ Kert ☺ Im T

A: Here given that a linear identifier T :ℙ2ℝ→ℝ3 defined by Ta+bx+cx2=a, b, a+b. We have to find Ker T…