45. Let f(x, y) = mxy², where m is a constant. Find a valuc of m such f(x, y)dA = 1, where R = [0, 1] x [0, 2]. that Activate Windows Go to Settings to activate Windows.

Q: If f(x, y, z) = ln(xª + yl0 + 2³) + V (x10 + y8 + z4), then find fr, fy and f; at (1, 1, 1).

A: The given function is fx, y, z=lnx4+y10+z8+x10+y8+z4 and the given point is (1, 1, 1). Evaluate fx…

Q: Find the maxamin s in flectlon Points and the in ter Vals on which the function inerease,decrease…

A: follow the solution which is mentioned in step 2.

Q: Then, the only positive equilibrium point of Eq.(1.1) is given by (2.7) (1 – A) (E Bi) Li=1 provided…

A: Given linearized equation of Eq(1.1) about y~ takes the form ;…

Q: Let f(x, y,z) = x² sin y + y e², where x =t + 3,y = net-1 and z = In 2t. dL at t = 1 is: 1-2n O -12n…

A: Given, fx,y,z=x2siny+yez, where x=t+3,y=πet-1 and z=ln 2t.   The objective is to determine dfdt at…

Q: Suppose that z is a differentiable function of x and y with dz (2, 5) = 108 and- dx dz (2, 5) = 9.…

A:

Q: Find fzyr. f(x, y, z) = x³y5₂6 + xy³ + yºz

A: Given: fx,y,z=x3y5z6+xy3+y6z We have to find fzyx For fzyx we first have to find the partial…

Q: b) Show that the “energy function" E(x, y) = 5 + is non-increasing along the solution, i.e., using…

A: (b) The objective is to show that the energy function  is non increasing along the solution, that…

Q: Let f(r, y, z) = ln(x² + z) + y²e#² – cos(2yz). Find fzyr- %3|

A: Consider,                                                                 f(x, y, z) = ln(x² + z) +…

Q: Suppose z = f(x, y), where f is differentiable, a = g(t), and y = h(t). If g(3) · fy( – 2, – 6) = –…

A: Find dz/st when t=3

Q: 4. Find the points on x² + y² + z² = 25, %3D where the temperature T(x, y, z) = x² + 4y² + 9z², is…

A:

Q: -Find the D.f ofr (x, y) = (x² – y)' at Po(3, 1) with

A:

Q: Let fn(x) = E s;(x) Y; be a linear smoother. Find a condition on the weights s;(x) so that fn(x) is…

A:

Q: 2Use divectional devivative delinihion of f(Hiy)=x y'at the divecionof ū =i jatthe Point (le2>

A:

Q: Suppose that z = f(x, y) is differentiable at the point (1024, 256) withf(1024, 256) = 2 and f,…

A:

Q: Consider the finction f(x, y) = 6y² + 4x² – 12xy – 4y. Then: O0,1) is a critical point and f has a…

A:

Q: Consider the finction f(x, y) = 6y² + 4x² – 12xy- 4y. Then: (1,1) is a critical point and f has a…

A: The given function is f(x,y)=6y2+4x2-12xy-4y

Q: Suppose that the only Införmation we have ab8ut a fuRcEiOH FIS y= f'(x) (a) Use a linear…

A: Given: f(1)=-7

Q: Suppose F(x,y)=sin²(xy +e"), where x=u² +v and y = In(u² +v). Find the . ƏF ¸ ÔF value of when u =1…

A: The given function is: F(x,y)=sin2xy+eywhere:x=u2+v         and         y=lnu2+v

Q: 교꾸가고 (a, y) + (0,0) (x, y) = (0,0) f(x, y) = x2+y2 is discontinuous at (0,0).

A:

Q: Let Use Euler's Method with h=.5 ond (X,Y.) -(1,1) to estimate (a, y )

A:

Q: 4. Suppose that F(t) is a differentiable function of one variable. Define the function z(x, y) = e'F…

A: z(x,y) ey F (exy )diff wrt xdzdx = ey F' ex/ye.1/yzx = ey.ex/yyF' (ex/y)and diff wrt ydzdy= ey…

Q: 2. Show that the function u = p(xy) + Vry ý(y/x) provides the equation n, = 0. dy? U -

A:

Q: If a and ß are positive constants, show that the particular solution of dy %3D У (В — ау) dt that…

A:

Q: Let r = x² + y – z and z³ – xy + yz + y³ = 1. Assume that x and y are independent ar is variables.…

A: Introduction :

Q: ) Find the linearization of f(x) = sinx at x = 0.(b) Compute dy if y = x2 +x and x changes from x =…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: 18. Use the Linear Approximation to f(x, y) = /x/y at (9,4) to estimate 19.1/3.9.

A:

Q: 1. Use the Chain Rule to find u and ou for w = x²y3 where x = dw at s2 +t2 and y = ds

A:

Q: Suppose z = f(x, y), where f is differentiable, x = g(t), and y = h(t). If g(5) = 8, g'(5) = 9, h(5)…

A: Given that z=fx,y, where f is differentiable. Here, x=gt and y=ht. Also, let, g5=8, g'5=9, h5=-7,…

Q: 2 2 If z = f(x, y), where x = s² - t² and y = t² s² and z is differentiable, then - Select one: True…

A:

Q: Let f (x,y, z) = xyz2 + 1 and suppose that x(t) = 2 – t, y(t) = In(t), and z(t) = 3t. df Use the…

A:

Q: 8.xy² If u = and error in x, y, z be 0.001, compute the maximum absolute and relative z³ error, when…

A: Given equation be u=8xy2z3 error in x, y, z be 0.001 Now ∂u∂x=8y2z3, ∂u∂y=16xyz3, ∂u∂z=-24xy2z4  and…

Q: Suppose z = f(x, y), where f is differentiable, x = g(t), and y = h(t). If g(4) = – 4, g'(4) = 9,…

A:

Q: 3. If f(x, y,z)= In *yz +e tar's="), find f,,fy and f. . хуz

A: we have to find the partial derivative

Q: 4. Let z = x2 + y³, x = 2st, y = s - t2, s = u", and t = u sin w. Compute for Oz ду and дw ди

A: Let z=x2+y3, x=2st, y=s-t2, s=uw, and t=u sin w.To compute for ∂z∂w and ∂y∂u.

Q: Let f (x, y, z) = ln(x2 + z) + y2 exz. Find fzyx

A:

Q: Suppose that the function f(x, y) has a critical point at (2, y) = (a, b). Furthermore, fæz (a, b)…

A: To decide the required conclusion, we use the second derivative test for maxima and mimima.

Q: Suppose that the joint p.m.f. of Y and Y2 is defined by: 2x + y for x = 1, 2,3; y = 1,2,3 54 f(x, y)…

A: The probability mass function of Y1 and Y2 is,

Q: Verify Young's Theorem S. f(x, y) = = e(2x+y) In(xy)

A:

Q: 0,tor o function frxyuppose that ond fy which is true lor the points Pll,D ond Qc1,2) where Pond…

A: Define D(x,y)=fxx(x,y)fyy(x,y)-[fxy(x,y)]2                                  =x2y2-22…

Q: 8. Let f(x, y) = cos(y – x) and r(t) = (e', e2t). Find if (r(t)) at t = ln(3).

A: The solution is given as

Q: 3. Determine if (х — 1)2, if x 1 is differentiable at x = 1.

A: Given  hx=x-12if x≤1x-1if x>1

Q: (ii)If y=(x+Jx* +1. prove that y'= Vx +1

A:

Q: Let f(x,y) = xcosy – ye*y. fry at (1,0)is equal to: -1 -5

A: fx is partial derivative with respect to x fy is partial derivative with respect to y

Q: Suppose that f(0) = 1, ƒ(0.5) = 2.5, f(1) = 2, and f(0.25) = f (0.75) = a. Using trapezoidal rule…

A:

Q: 1. Let z = f(x, y), find for: and dy - - (a) e"y + z ln y = 0 (b) yz – sin z = xy

A:

Q: 3. Suppose that z = f(x, y) is a differentiable function with respect to variables !! x and y and is…

A:

Q: 12. Suppose that f(x, y, z, w) = 0 and g(x, y, z, w) = 0 determine z and w as differentiable…

A: (12) Consider the provided question,

Q: 2. Let f(x,y) 3x y. If C is the line segment from (1,1) to (2,3), evaluate r'dt.

A:

Q: Given F(x, y) = (2xe'6(y), e'x²(eY + 0(y)) with o E C'(R) then O (A) F is conservative only if o(y)…

A: (A ) is true.