Let f(x, y) = mxy , where m is a constant. Find a value of m such that R f(x, y) dA = 4, where R = [5,7] × [1,2]. Use symbolic notation and fractions where needed.) m =

Q: 10. If z = x + f(u), where u = xy, show that dz = x. х дх

A:

Q: If f(x,y) = x In(2y³ – 5) + y e* , find ! of and ôx ây

A:

Q: if z=xarctan(y/z), find ∂z/∂x at x=0, y=1, z=1

A:

Q: ди ди ди for u = az Find p-q if p= x+ y+ z ,q = x + y + z ,r = = (V3,2,1). and ax' əy 9-r x + y - z…

A: Q3. Given that                                            u=p-qq-rp=x+y+zq=x+y+zr=x+y-zPoint, (x, y,…

Q: derrorsinx,y,zbe0.001.Find relative error when x = y = z = 1.

A: Given,                 U=z4                                                  ...(1)  x=y=z=1, and…

Q: Given: WX 1 XZ, YZ 1 ZX, WZ = YX Prove: ΔWZX ΔΥXΖ Y W

A:

Q: (b) If V'u =0 for x2 0 and if u f(y) on x=0, Show that ,y): +(y-5)

A:

Q: If f(u, v, w) is differentiable and u = x - y, v = y - z, and w = z – x, show that fe af af + = 0.…

A:

Q: of af and Let f(x, y, A) = xy + A(5 – x – y). Find· ax' əy` af

A: f(x,y,λ)=xy+5λ-λx-λy .....(1) Differentiating (1) partially with respect to x, ∂f∂x=(1)y+0-λ-0…

Q: Let z = ƒ(u, y), u = ax + by, and y = ax - by. Express z x and zy in terms of fu , f y, and the…

A:

Q: Given that vec F =x^ 2 y hat i -(z^ 3 -3x) hat j +4y^ 2 hat k find the k- component of ( nabla* vec…

A:

Q: For x,y E [0,1], prove that xy(1-x-y)≤1/27

A:

Q: 4) Suppose that T : R³ → R² is defined by T((x, y, z)) = (1+2x – z , 3 – x + 6y) Is T linear?…

A:

Q: Given f(x,y) = ex cos y, Evaluate fx(2,0)

A:

Q: Given f(2, y, z) =v V-I - 2y + z, find f.(z, y, z) = f(z, y, z) = f(1, y, z) =

A: We will use definition of differentiation. First we will handle derivative of the root of the…

Q: If f(1, y, 2) = In(z³ + y8 + z³) + V(z³ + y³ + z³), then find fr, fy and fa at (1, 1, 1).

A:

Q: Let r, y EN such that y # 0, then y+r#0.

A:

Q: Let x, y € R" be given. (a) If ||z||||y||=1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1 and ||y||…

A:

Q: f({x, y))) for all c e R and all (x, y) E R?

A:

Q: (a) Vx E R, 3y E Z such that y > x + 110. (b) Vx E Z, 3y E N such that y > x + 110. (c) 3x E Z such…

A:

Q: ; Let x, y ER" be given. (a) lf ||x|| = ||y|| = 1 and x - y = 1, show that x = y. (b) If ||x|| ≤ 1…

A:

Q: 10. If z = x + f(u), where u = xy, show that дz dz х дх = x. ду

A:

Q: Compute the discriminant D(x, y) of the function. f(x, y) = x' + yt – 6x – 2y² + 1 (Express numbers…

A:

Q: How to solve this?

A: We are given that x + y + z = 5 where x, y, z ∈ R. Now, we need to prove that x2 + y2 + z2 ≥ 5/3.…

Q: For x = 1, 2, 3 and y = 1, 2, let the joint pmf of X and Y be defined by fX,Y (x, y) = x + y/21…

A: Solution

Q: Let x, y ∈ R. Suppose x2 + y2 = 0. Prove that x = 0 and y = 0.

A:

Q: Given f(r, y, z) = – 5e 4ayz, find %3D fr(x, y, z) = f,(x, y, z) = f:(2, y, z) =

A:

Q: Find and d?z and prove that 2 0²z IF 2 = f(xt ay) + F CX-ay) %3D

A:

Q: Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find ∂z/∂t.

A: Solution:- The given question is  Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find…

Q: 3. Given z =, show that ху xy(zxx + Zyy) уз — х3 2 || x²y2

A: δwδt=δwδxδxδt+δwδyδyδt+δwδzδzδt       =ysin(z2).(-1)+xsin(z2).0+2xyzcos(z2)(2t)

Q: If Z = x.n. f (), then show that: x. Zx + y.Zy = z

A:

Q: Given f(x, y, z) = √x2 - z+ 1 = ду 2Va²-z o af Х - z ду ala ala ду = Vx2 ет - У - у2 Y Determine af…

A:

Q: For x, y E [0, 1], prove that 1 xy(1 – x – y) < 27

A:

Q: Q: If u =f(x² +2yz, y² + 2=x)Prove that (y-ax

A: Step by step compute the derivative with respect to each variable x,y or z. Then substitute it in…

Q: ди Ifu=r(x* +2yz,y* +2zx)Prove that (y -zx) +(x² - 3z) + (:* - xy) ZX

A:

Q: Let z, w E C. Show that zw = 0 implies z = 0 or w = 0. %3D

A:

Q: For x, y, z, w > 0, prove that (x/z)+(y/z)+(z/w)+(w/x)≥4

A: It should by x/y, instead of x/z

Q: Q3/ prove fry = fyx if f(x,y) = x + xy – 5x³ + In(x2 + 1)

A:

Q: Let F(x, y) = xy + 2y² + 20x + 6y + 33. Find all values of y such that F(y, y) = –2.

A:

Q: For x = 1, 2, 3 and y = 1, 2, let the joint pmf of X and Y be defined by fX,Y (x, y) = x + y/21…

A: Solution

Q: If X is a RV with f(x) = 0, when x 0, P(X 2 a) <u/a. %3D

A:

Q: Given f(x, y, z) = x In(yz³), find fay and fyz. %3D

A:

Q: S_f(x.y,z)ds

A: The solution is given as

Q: Let f(x, y) = x² + y2 + 2x + 4 and P,(-1,0) then Vfle, is i – j. True False

A:

Q: 4) Let f(r, y, z) = In(r + 2y + 3z). Find Vf = . %3D

A: Given: f(x, y, z)=ln (x+2y+3z)

Q: . If z = f (x, y), where x = e" - e and y = e - e", show that TM UT az x: az az az dy ax UTM UTM UTM…

A:

Q: If F(x,y, z) = (5x – y + az)î + (bx + 2y + 5z)ĵ + (2x + cy – z)k is irrotational then find the value…

A: Explanation of the answer is as follows

Q: f(z) =z? is discontinuous

A: f(z)= z2 is a polynomial function in z and polynomials are continuous everywhere.

Q: Find f, and f and evaluate each at the given point. F(x, y) = e*y?, (In 4, 2) f(x, y) f,(x, y) =…

A: