Confirm that ϕ is a potential function for F(r) on some region, and state the region. a ϕ ( x , y ) = tan − 1 x y F( x , y ) = y 1 + x 2 y 2 i+ x 1 + x 2 y 2 j b ϕ ( x , y , z ) = x 2 − 3 y 2 + 4 z 2 F( x , y , z ) = 2 x i − 6 y j+8zk
Confirm that ϕ is a potential function for F(r) on some region, and state the region. a ϕ ( x , y ) = tan − 1 x y F( x , y ) = y 1 + x 2 y 2 i+ x 1 + x 2 y 2 j b ϕ ( x , y , z ) = x 2 − 3 y 2 + 4 z 2 F( x , y , z ) = 2 x i − 6 y j+8zk
Find and sketch the domain of the function
f(x,y) = cosx + V3x-y+2
1.
(+y + ) (1+? + +)
9. Integrate the function f(r,y, 2) =
over the
entire 3D coordinate system, i.e., all of R'.
Plot the function f(x, y) = x² – y² over the square region bounded by the lines y =x - 2, y=x+2,
y = -x – 2, and y = -x + 2. Then integrate f over this square region.
Precalculus: Mathematics for Calculus - 6th Edition
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