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Chapter 14: Q. 27 (page 1096)

Sketch the vector fields in Exercises 25–32.
$F (x, y) = i + j$

Short Answer

Expert verified

Sketch of the vector fields is

Step by step solution

01

Step 1. Given Information

We have to sketch the vector fields in the given exercises .

$F (x, y) = i + j$

02

Step 2. The given vector field F(x,y)=i+j

The graph of the vector field is

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Most popular questions from this chapter

Find

$\begin{aligned} \int_{S} F (x, y, z) \cdot n d S if \\ F (x, y, z) = \frac{\ln (x^{2} + y^{2} + 1)}{z + 3} i + \frac{y}{y + 1} j + e^{z^{2}} k \end{aligned}$

Where S is the portion of the sphere with radius 2, centered at the origin, and that lies below the plane with equation $z = - \sqrt{2}$ , with n pointing outwards.

$F (x, y, z) = 5 i + 13 j + 2 k$ , where S is the unit sphere, with n pointing outwards.

Evaluate the integrals in Exercises 43–46 directly or using Green’s Theorem.

\iint_{R} (3 x y - 4 x^{2} y) d A

, where R is the unit disk.

Use the same vector field as in Exercise 13, and compute the k-component of the curl of F(x, y).

Given a smooth surface S described as a function z = f(x, y), calculate the upwards-pointing normal vector for S.

See all solutions

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