2. Let i = y?x + xŷ + z²ż, and let S be the paraboloid z = x2 + y? with 0 < z < 1. Show that fci. de = fsỹ x ī - dŠ by evaluating each term separately.

Q: Let Z = (1, 1, 2) be a point in R³. Find the closest point to Z tha lies on the plane give by -x+y-z…

A: The normal vector to the plane is &lt;-1, 1, -1&gt;. The point you seek would have to be some…

Q: y(6) – 4y®) +6y® - 4y'+y =7

A: Answer

Q: 15. z+i · (z − 1 − i)³(z − i) JR-1 dz

A:

Q: Evaluate SSS e² dV where E is enclosed by the E paraboloid z = 1 + x² + y², the cylinder x² + y² =…

A:

Q: Consider the simple linear model Y; = Bo + B1Xi + €¿, where e~N(0,0²); i = 1,2, .. 1. Show that a)…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts(a, b-i,…

Q: 11. Find an equation of the tangent plane to the surface Va+Vy+Vz=4 at the point P(4,1, 1). 12. Find…

A:

Q: Let A = (1,1) and B = (1,5) be in the Poincar ́e plane. Find C = (xC,yC) for which xC > 1 and…

A: The natural point that comes in our mind is (2,6).

Q: 3. (.J 6) For two vectors u = [1,0,0]" and v = [1,1, 1]", find a third vector with unit length such…

A: Given: Lt us consider the given, u→=1,0,0v→=1,1,1

Q: seclyltun Cy) -csc?(y!dy

A: Use formulas of integration to evaluate the given.

Q: (b) Prove that Vx, y ≤R : x² + xy + y² ≥ 0, and that x² + xy + y² = 0 if and only if x = y = 0.…

A:

Q: 3) Express aw/ar and aw/as in terms of r and s if w = x +2y+z², x = 5, y = r² + Ins, z = 2r

A:

Q: Evaluate SdV where G is enclosed by the paraboloids z = G z = 4 x² - y². Answer: 2π 3x² + 3y² and

A:

Q: ulo,3) = 1+ y 1) u'xg U(x, o) = 1+x 2

A:

Q: əz əz 1. Let z = x² + y³, x = 2st and y = s − t². Compute for and əx Ət

A:

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

A:

Q: Q.1) Use the polar integral to evaluate 2 dydr 71+ Vr2 + y?

A:

Q: 2. Find a unitvedctor with positive z-component porpendcular to the plane 2xt2y-2=3 Z-C

A: We will find out the required value.

Q: e the Cauchy problem y' = y cosx, y(0) = 1.

A:

Q: Substitute r = 1 into + p(z)y=f(z)y and show the result is linear. Write your answer in linear…

A:

Q: Differentiate w.r.to "x" y = xsin-1x +x/(1-x3)

A:

Q: ndwritten please Rew

A: Introduction: A Boundary price drawback may be a system of normal differential equations with…

Q: Find minimum perpendecular distance between given paraboles. y = x2 + 1 y = x - x2

A: To find the minimum distance between 2 parabolas

Q: x2 + 4y? – xy + 6x – 5y + 1. -

A:

Q: 4. Use the method of Lagrange Multipliers to find the point on the plane r+y- 2 = 5 that is closest…

A: Given: The plane equation is x+y-z=5 and the point is -3, 5, 4.

Q: 3y², Compute divà and curlà for à = (x²y²z?)î – (2xy² – 16x)ĵ + (9_)&.

A:

Q: 4. Find the unit bivector for the plane z = x+y. Where xe₁+ ye2 + zez denotes an arbitrary point on…

A: As per the question, we are asked to determine the unit bivector for the plane defined by the…

Q: use implici't differen tiatiom to brind dyldu at the pont (2,2) = 1+y" エ+Scu

A:

Q: 6. Evaluate S (x² + y²) ³/2 dydx where D is the disc x² + y² = 4. Show your work!

A:

Q: B. Let z- ( x-y)e×y (x-y)exy Show: Zxx + zyy + exy Cya-x3)= -z (xy+ 2)

A: Partial derivative of a function z=f(x,y) with respect to x is the derivative of z keeping y…

Q: Let C be the rectangle in the xy-plane with vertices (0,0), (1,0), (0, 2) and (1, 2), and let F(r,…

A: