Determine whether the statement is true or false. Explain your answer. Suppose that z = f x , y has continuous first partial derivatives in the interior of a region R in the x y -plane , and set q = 1 , 0 , ∂ z / ∂ x and r = 0 , 1 , ∂ z / ∂ y . Then the surface area of the surface z = f x , y over R is ∬ R q × r d A
Determine whether the statement is true or false. Explain your answer. Suppose that z = f x , y has continuous first partial derivatives in the interior of a region R in the x y -plane , and set q = 1 , 0 , ∂ z / ∂ x and r = 0 , 1 , ∂ z / ∂ y . Then the surface area of the surface z = f x , y over R is ∬ R q × r d A
Determine whether the statement is true or false. Explain your answer.
Suppose that
z
=
f
x
,
y
has continuous first partial derivatives in the interior of a region R in the
x
y
-plane
,
and set
q
=
1
,
0
,
∂
z
/
∂
x
and
r
=
0
,
1
,
∂
z
/
∂
y
.
Then the surface area of the surface
z
=
f
x
,
y
over R is
Suppose that D is the ellipse
D={tr, ») € R°: + v* < 10}
{(x, y) € R²:
+ y? < 10}
D =
4
and that f is a differentiable function defined on all of R². Suppose that (xo, Yo) is in
ƏD, the boundary of D. Denote by (xo, Yo) the derivative of ƒ in the direction of the
outward pointing unit normal at the point (xo, Yo). Given that
fe
(4, 3) = 2 and
df
(4, 3) = 2,
dy
calculate (4, 3).
Let z = g(x, y) = f(3 cos(xy), y + e") provided that f(3, 4) = 4, f1(3, 4) = 2, f2(3, 4) = 4.
%3D
i) Find g1 (0, 3).
i) Find g2 (0, 3).
i) Find the equation of the tangent plane to the surface z = f(3 cos(xy), y + e#') at the point (0, 3).
Türkçe: f(3, 4) = 4, f1(3, 4) = 2, f2(3, 4) = 4 olmak üzere z = g(x, y) = f(3 cos(xy), y + e™") olsun.
%3D
%3D
i) 91 (0, 3) değerini bulunuz.
ii) 92 (0, 3) değerini bulunuz.
iII) z =
f(3 cos(ry), y + e#") yüzeyine (0, 3) noktasında teğet düzlemin denklemini bulunuz.
O i) 12, ii) 4, iii) 12x + 4y - z = 8
i) 12, ii) 4, ii) 12x - 4y - z = 0
O i) 12, ii) 12, iii) 12x + 12y + z = 32
O i) 36, ii) 4, iii) 36x - 4y - z = -28
O i) -24, ii) 12, iii) -24x + 12y + z = -16
) 36, i) -8, ii) 3бх -8y - z3D -16
O i) -12, ii) -8, iii) -12x -8y - z = 8
О) -24, i) 16, i) -24x + 16у -z%3D 8
Calculus, Single Variable: Early Transcendentals (3rd Edition)
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