Let F(x,y,z) = (x +y+z²)k and let S be the boundary of the cylinder x² ₂2 + y² ≤ 4 and 0 sz≤3. Calculate 11,0 where n'is the normal pointing outside the cylinder. S FndS

Q: 8. What is the minimum value of the function defined by y = cosx + 4? В. З A. 2 C. 4 D. 5

A: Given- y=cosx+4 To find- The minimum value of the expression.

Q: y 2. JJp x5+1 dA, D = {(x,y)|0 < x < 1,0 < y<x²}

A:

Q: e /// 2 Evaluate 2xz dV where E {(x, y, z) |1 ≤ x ≤ 4, r ≤ y ≤ 2r, 0 <z<x+3y}

A:

Q: 17. Find the average value of f(x, y) = 2x – y, where 0 sxs 2 and 2 s ys 3.

A: Solution:Given f(x,y)=2x-yfor 0≤x≤2, and 2≤y≤3to find the average value of…

Q: Let a differentiable function g and f(x,y) = g(x²y²), g(4) = 4, g'(4) = 1 be given. Then, find the…

A:

Q: Let a differentiable function g and f(x,y) = g(x²y²), g(4) = 4, g'(4) = 1 be given. Then, find the…

A:

Q: The function u is the temperature at (x, y) throughout a thin rectangular plate witl Shae x = 0, x =…

A: Steady state temparature is the temperature when time tends to infinity. In other words it is…

Q: I, FIND HE NET AREA OF fos) - Zx and gx)= O FROM [-3,3]

A: Given : Functions f(x) = 2x and g(x) = 0   To find : Net area of f(x) and g(x) from [-3,3]?

Q: 5. f(x, y) = (y — x²)(y — 2x²). - Ans.: no extrema, saddle at (0, 0)..

A:

Q: Find the integrating factor of : zydz = (x² + 2y²) dy 1 a. µ 2у3

A:

Q: Let f= 2zy + yx, v= [y, z, 4z -x]. Find Dyf at (2,1,2). NOTE: Enter an exact answer. Dvf (2, 1, 2) =

A: Given: fx, y, z=2zy+yx, v=y, z, 4z-xTo find: The directional derivative, Dvf at 2, 1, 2

Q: Let u- (3i - 3) and u (i +3). Let f(z, v) be a differentiable function, such that D, f = 3//10, Du,f…

A:

Q: Find the extrema and/or the saddle points of the functions a) f(x, y) = ex cos y b) f(x, y) = x² +…

A: Note: As per the honor code, the first question can be answered since the exact one wasn’t…

Q: af Let f(x, y, z) = xy + z². Calculate where x = = s², y = 2st, z = t². მs

A: Step 1: Step 2:

Q: af and . Given f(x, y) x'+ y find dx ' dy' axdy дудх

A:

Q: lo nierob xiv) Is T onto? Explain your reasoning. noto xv) Find a basis for the kernel of T. Twi lo…

A: See the detailed solution below.

Q: Find the equation for the tangent plane to the surface x2 - 5xyz + y² = 7z2 at the point (-1, -1,…

A: Simplify the given equation of the surface in the form F(x,y,z)=0. x2-5xyz+y2=7z2x2-5xyz+y2-7z2=0…

Q: Find fy, fy, and f,, and evaluate each at the given point. X' Z' f(x, y, z) = xy + 2xyz – 8yz, (-3,…

A: Using partial differential equation, we can find required results

Q: If f(x,y,z) = 2x² − yz + xz², where x = 2 sint, y = t² − t + 1, and z = e−³t, find f't)

A: from chain rule of derivaties…

Q: Let w=x² +3y² + 2z² where x=rcos, y=rsin 0,z=5t find dw dw ar' at

A:

Q: Let z = In(x² + y²) be a differentiable function of x and y, where x = sin t, y = cos t. dz when t =…

A:

Q: Compute F-dS for F = (sin(y), sin(z), yz), S being the rectangle 0 ≤ y ≤ 4,0 ≤ z ≤ 5 in the yz-plane…

A: According to the given data, find the :

Q: ) Find MThe equation of The normal to 5 at the point (a, 4) y=dx

A: Given curve is x2+y2=5. To find the equation of normal at the point (2,1). Solution: Given curve is…

Q: dw at (u,v) = (1, 5) for the function w(x, y) = xy - y; x = u - v, y = uv. Evaluate du -65 O 4 0000

A: Given:    wx,y=xy-y2              x=u-v              y=uv

Q: Find fzya. 4.73 f(ar, y, 2) = a*y"z³ + xy$ + y®z .6 zyx

A:

Q: Let f(x, y) = 6e sin(7y) af af dy

A:

Q: . Let u = [1, 7, 4]), v = [1,5, 5), and w [35, 25, 20]. Find the critical point of f(x, y) = (x · u…

A:

Q: Let f(x) = f(x)= 2 x* +x* – 6x³ +4x.

A:

Q: 1. Let f(u, v) be a continuously differentiable function. Let u = e*, v = e³. Show that u²fuu + v²…

A: Given that f(u,v) is a continuously differentiable function, and u=ex, v=ey then show that…

Q: Q.2 Find curlF at point (1,0,0) where f(x, y, z) = xe*y + y + 2

A:

Q: Find X only using Crammers rule 2x+リ-「Z=D2 x2 -y +VZ 2 x? +2y +VN= 4

A: