Find Mx, My, and (x, y) for the lamina of uniform density p bounded by the graphs of the equations. y = -x² + 3x + 6, y = x + 6 Mx My (x, y) = = =

Q: Find the absolute maximum and minimum values of the function f (x, y) = x – y + xy on the closed…

A:

Q: Show that the function f(x,y) = x³ + y³ – 63(x +y) + 12xy is maximum at (–7,–7) and minimum at…

A: Given function: fx,y=x3+y3-63x+y+12xy Formula Used: D-Test: For each point a,b where fxa,b=0 ,…

Q: Find fzyx. 8.8 f(x, y, z) = x*y°z® +xy³ + y°z f zyz ||

A: GIVEN: f(x, y, z) = x4 y8 z8 + xy5 + y5 z

Q: Suppose that the Second Derivatives Test is applied to a real-valued function z = f(x, y), whose…

A: Given real value function is z=f(x, y) and second derivatives are continuous on the disk D centered…

Q: et f(z, y) = for (z, y) # (0,0). Find the level curves of 2 + y²

A:

Q: Gy Determin thle area between the curve 9 = x²+1 and y+ X = 7

A: Given: To determine the area between the curve y=x2+1 and y+x=7⇒ y=7-x

Q: Find the local minimum value of f(x, y) = 4+ x³ + y³ – 5xy.

A: Explanation of the answer is as follows

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: Let r(t) = (cost,sin t, ln(cost)).Find T, N, and B at (1, 0, 0).

A: Let rt=cos t, sin t, lncos t at 1,0,0 Find T, N and B. Tangent vector to the curve is denoted by…

Q: Find the global extrema of f(x, y) = x3 - xy - y2 + y on the square [0, l] x [0, 1]

A:

Q: Find the direction of maximum decrease of the function f(x, y, z) =exyz at the point P(1,1,1) and…

A: Given function is

Q: c) Integrate the function f(x, y) bounded by the lines y = x, y = 2x. x = 1. r = 2. over the region…

A: Integration over the said region

Q: Find the absolute maximum and minimum values of D(x,y)=x²-xy + y² + 1 On the closed triangular plate…

A: Here I am using basic calculus we and also use short method.

Q: For F(x, y,z)=(6xsin y+10xz' )i+(3x cos y-4ye"-2y ze" ) j+(-2y'e* +15x²z² )k , find | a function f…

A:

Q: Find a strict Liapunov function for the equilibrium point (0,0) of x = -2x – y y = -y– x. Find 8>0…

A: Given :-  A strict Liapunov function for the equilibrium point (0,0) of  x’ = -2x-y2 y' = -y-x2 To…

Q: (c). If y = f(x1, x2, u, v), where x =h(u, v) фу and- pu Find total derivative Also draw their…

A: