Determine whether the statement is true or false. Explain your answer. If f has continuous first partial derivatives in the interior of a region R in the x y -plane , then the surface area of the surface z = f x , y over R is ∬ R f x , y 2 + 1 d A
Determine whether the statement is true or false. Explain your answer. If f has continuous first partial derivatives in the interior of a region R in the x y -plane , then the surface area of the surface z = f x , y over R is ∬ R f x , y 2 + 1 d A
Determine whether the statement is true or false. Explain your answer.
If
f
has continuous first partial derivatives in the interior of a region
R
in the
x
y
-plane
,
then the surface area of the surface
z
=
f
x
,
y
over
R
is
Use the definition V = ( ) to prove the identity: curl (curl F) = grad (div F) – V²F
Assume that F(x, Y, z) = (P(x, y, z), Q(x, y, z), R(x,y, z)) has continuous second partial derivatives.
Hints: plug in F = (P,Q, R) into each side of the equation, take a lot of partial derivatives, and show that the two sides are equal.
8² R
8º R
Also: 7²F stands for (V · V) (F)., so as a vector really V²F = i ( +.
a P
+j
Find the surface area of the surface when f(x)=x3 on [0,2]. Is rotated about the y-axis and about the x axis on [0,2]
The slope of the surface z = xy² in the x-
direction at the
point (2, 3) is
O 12
O 8
O 11
O 9
O 10
Precalculus: Mathematics for Calculus - 6th Edition
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY