*Show that for any x, y ER² we have doo (x,y) ≤ d2(x, y) ≤ di(x, y). Undez d2(x, y)? Under what conditions is what conditions on x and y is doo (x, y) d2(x, y) = d₁(x, y)?

Q: SV² + 1)dy у2 +4

A: The meaning of the expression ∫(y2+1)dy/(y2+4) is that the indefinite integration of y2+1 is to be…

Q: W(s, t) = F(u(s, t), v(s, t)), where F. u. and v are differentiable. If u (6,-6)= -2, u,(6, −6) = 3,…

A: The objective of the question is to find the partial derivatives W_s(6,-6) and W_t(6, -6) for the…

Q: prove if x → y then xor y = y =

A: To prove : If x→y then x or y = y Lets use the help of truth table to prove the above statement.

Q: If the substitution u = √x + 1 is made, the integral 3 A S u² u² - 1 du B du 3 2u²2 u² - 1 √ √x+1 dx…

A: We solve the given problem by using the substitution method.

Q: Evaluate |[[p(4z + 3y² + 2x)dV = {(x, y, z) | 0<x < 2,0 sys 2, 0 s z < 1} .

A: We have to evaluate the triple integral given below: ∭B4z3+3y2+2xdV  Here, the region B in three…

Q: /1- (z² + y²) dz dy dæ ) Evaluate

A:

Q: Solve the differential equation using Method of Undetermined Coefficients and by Inspection. (D³ +…

A:

Q: 2. If F(x, y, z) = 2z3 – 3(x² + y²)z, then verify that Frx + Fyy + F2 = 0. %3D

A:

Q: If Iz – 2| < 2, then find (x,y) * arg(z),r i5

A:

Q: What are the coordinates of C' after its preimage, C(5,-3), is reflected over the x-axis? O (5,3) O…

A:

Q: Determine R (H) if R'(4) - . R

A: We have to find vector R(t).

Q: + x(x*+ zy² + ig) dy= luy) dy 2. 2. 2) 3(x y) dx -

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 3. Given fxx(x,y)= 4x² On Support 0 Otherwise Let U=Y-X. Determine f(u) (Including the Support of U)…

A:

Q: If f(z) = z² − (z)² + zz, calculate the following: a) u(x, y) and v (x, y) b) u(-10,-5) and…

A:

Q: Evaluate y ds, C: x = t², y = t, - 1<t < 9 |3D (325)-(5)를 1 12

A:

Q: The given functions are concave or convex or neither in the domain: 1). f(x, y) = 2r-y-r²+2ry-y² 2).…

A: As per the question we are given two multivariate quadratic equations : f(x,y) = 2x - y - x2 + 2xy…

Q: Verify that 2²4 ахду 22+ ду ах - for f(x, y) = 2x³y6 - 4x5y4.

A:

Q: 3. If z = f(x, y) with the relation xy²z³ + x³y?z +1 = x + y+ z. Find dz at (1, 1, 1).

A:

Q: P = (x, y) = x + 4y ≤ 13 3x + y ≤ 6 x ≥ 0, y ≥ 0.

A: Let us first find the feasible region.

Q: FI = r Where f(r) = -i = 2xi – 3yj + zk So be it %3D div) grad(f) find

A:

Q: Se xye" dy, C. x- , y-, z- , 0 <te1

A:

Q: 1 x+R+ 2)²(x+ x+ R+ 4) dx (Hint: Let u= x+R+2 x+R+4

A: ∫1x+R+22x+R+42dx

Q: b) If it is possible, find the function f(x, y) = u(x, y) + iv(x, y). where u(x, y) = x2 + 2xy- y²…

A: That's easy. Have a great day!!!

Q: Is (Vx)(V)x=y → (Vy)y = y an instance of Ax2? V b. Prove the following: (Vx) (Vy)x = y → (Vy)y = y…

A:

Q: Find the values of af /ax and af lay at the point (4, 5) if f(x,y)=x² + 3xy + y -1

A:

Q: when that this 1x² + y² Shothathis sho (x, y) (0,0) and f(0,0) function is continous at (0,0)

A:

Q: for 3x'z -x'y² +2z + 3xy = 0 ( Hint: Let %3D F(x,y,z) = 3x z - x'y? + 2z +3xy) %3D

A: Explanation of the answer is as follows

Q: 9. Find div F if F(x, y, z) = x²yi + xyzj - x²y²k. A. 2xy + yz - 2xy² B. x² + xy C. 2xy - xz D. 2xy…

A:

Q: 6) Show that (2xy, 2yz + x², y²) is conservative.

A:

Q: 16. Where does the smallest value f(r, y) + 3ay + y occur on the rectangle (-2, 2) x (-3, 1]? a) It…

A:

Q: W(s, t) = F(u(s, t), v(s, t)), where F. u. and v are differentiable. If u (6,-6)= -2, u,(6, −6) = 3,…

A: The objective of the question is to find the partial derivatives of W with respect to s and t,…

Q: Suppose that it + [[ f(x, y)dA - 26 and ₂⁹(2, 3)dA R R (A) The value of [kf(x, y) + g(x, y)]dA is […

A:

Q: 2 2 ex: f(x, y, z) = x² - by ² fx (x, y, z) = fy(x, y, z) = fz(x, y, z) = 2 ezete

A: f(x, y, z) = (x2 - 6y2)/(y2 + 2z2)    =&gt; fx(x, y, z) = ∂/∂x [(x2 - 6y2)/(y2 + 2z2)]…