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Chapter 14: Q. 5 (page 1119)

Compute a general formula for dS for any plane $a x + b y + c z = k i f c \neq 0 .$

Short Answer

Expert verified

a

Step by step solution

01

Step 1. Given Information.

Given a plane equation: $a x + b y + c z = k, a n d a l s o c \neq 0 .$

02

Step 2. General formula for dS.

a

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Most popular questions from this chapter

Integrate the given function over the accompanying surface in Exercises 27–34.
$f (x, y, z) = \frac{y}{x} \sqrt{4 z^{2} + 1}$ , where S is the portion of the paraboloid $z = x^{2} + y^{2}$ that lies above the rectangle determined by $1 \leq x \leq e$ and $0 \leq y \leq 2$ in the xyplane.

$Compute the divergence of the vector fields in Exercises 17 - 22 . G (x, y, z) = (x^{2} + y - z) i - 2 y \cos zj + e^{x^{2} + y^{2} + z^{2}} k$

Find the areas of the given surfaces in Exercises 21–26.

Sis the portion of the surface determined by $x = 9 - y^{2} - z^{2}$ that lies on the positive side of the yzplane (i.e., where $x \geq 0$ )

What are the outputs of a vector field in $ℝ^{3}$ ?

Why is $d A$ in Green’s Theorem replaced by $d S$ in Stokes’ Theorem?

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