(a) The vector assigned to the given point by the given vector field.

Question

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Answer 1

Question

Chapter 16, Problem 1CRE

To determine

(a)

The vector assigned to the given point by the given vector field.

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 - 3 (5), 5 - (- 3) 〉 = 〈 - 15, 8 〉$

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 x y, y - x 〉$

Calculation:

Here, $\vec{F} = 〈 x y, y - x 〉$

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 - 3 (5), 5 - (- 3) 〉 = 〈 - 15, 8 〉$

To determine

(b)

The vector assigned to the given point by the given vector field.

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by $\vec{F} = 〈 4, 8 〉$

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 4, 8 〉$

Calculation:

Here, $\vec{F} = 〈 4, 8 〉$

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 4, 8 〉$

To determine

(c)

The vector assigned to the given point by the given vector field.

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 9, 1 〉$

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 3^{x + y}, \log_{2} (x + y) 〉$

Calculation:

Here, $\vec{F} = 〈 3^{x + y}, \log_{2} (x + y) 〉$

Vector assigned to the point P(–3, 5) is given by

$\begin{array}{l} \vec{F} = 〈 3^{- 3 + 5}, \log_{2} (- 3 + 5) 〉 \\ = 〈 3^{2}, \log_{2} (2) 〉 \\ ∴ \vec{F} = 〈 9, 1 〉 [∵ \log_{2} (2) = 1] \end{array}$

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Students have asked these similar questions

(12 points) Let E={(x, y, z)|x²+ y² + z² ≤ 4, x, y, z > 0}. (a) (4 points) Describe the region E using spherical coordinates, that is, find p, 0, and such that (x, y, z) (psin cos 0, psin sin 0, p cos) € E. (b) (8 points) Calculate the integral E xyz dV using spherical coordinates.

(10 points) Let f(x, y, z) = ze²²+y². Let E = {(x, y, z) | x² + y² ≤ 4,2 ≤ z < 3}. Calculate the integral y, f(x, y, z) dV.

(14 points) Let f: R3 R and T: R3. →R³ be defined by f(x, y, z) = ln(x²+ y²+2²), T(p, 0,4)=(psin cos 0, psin sin, pcos). (a) (4 points) Write out the composition g(p, 0, 4) = (foT)(p,, ) explicitly. Then calculate the gradient Vg directly, i.e. without using the chain rule. (b) (4 points) Calculate the gradient Vf(x, y, z) where (x, y, z) = T(p, 0,4). (c) (6 points) Calculate the derivative matrix DT(p, 0, p). Then use the Chain Rule to calculate Vg(r,0,4).

Answer 2

Question

Chapter 16, Problem 1CRE

To determine

(a)

The vector assigned to the given point by the given vector field.

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 - 3 (5), 5 - (- 3) 〉 = 〈 - 15, 8 〉$

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 x y, y - x 〉$

Calculation:

Here, $\vec{F} = 〈 x y, y - x 〉$

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 - 3 (5), 5 - (- 3) 〉 = 〈 - 15, 8 〉$

To determine

(b)

The vector assigned to the given point by the given vector field.

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by $\vec{F} = 〈 4, 8 〉$

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 4, 8 〉$

Calculation:

Here, $\vec{F} = 〈 4, 8 〉$

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 4, 8 〉$

To determine

(c)

The vector assigned to the given point by the given vector field.

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 9, 1 〉$

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 3^{x + y}, \log_{2} (x + y) 〉$

Calculation:

Here, $\vec{F} = 〈 3^{x + y}, \log_{2} (x + y) 〉$

Vector assigned to the point P(–3, 5) is given by

$\begin{array}{l} \vec{F} = 〈 3^{- 3 + 5}, \log_{2} (- 3 + 5) 〉 \\ = 〈 3^{2}, \log_{2} (2) 〉 \\ ∴ \vec{F} = 〈 9, 1 〉 [∵ \log_{2} (2) = 1] \end{array}$

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Answer 3

Question

Chapter 16, Problem 1CRE

To determine

(a)

The vector assigned to the given point by the given vector field.

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 - 3 (5), 5 - (- 3) 〉 = 〈 - 15, 8 〉$

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 x y, y - x 〉$

Calculation:

Here, $\vec{F} = 〈 x y, y - x 〉$

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 - 3 (5), 5 - (- 3) 〉 = 〈 - 15, 8 〉$

To determine

(b)

The vector assigned to the given point by the given vector field.

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by $\vec{F} = 〈 4, 8 〉$

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 4, 8 〉$

Calculation:

Here, $\vec{F} = 〈 4, 8 〉$

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 4, 8 〉$

To determine

(c)

The vector assigned to the given point by the given vector field.

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 9, 1 〉$

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 3^{x + y}, \log_{2} (x + y) 〉$

Calculation:

Here, $\vec{F} = 〈 3^{x + y}, \log_{2} (x + y) 〉$

Vector assigned to the point P(–3, 5) is given by

$\begin{array}{l} \vec{F} = 〈 3^{- 3 + 5}, \log_{2} (- 3 + 5) 〉 \\ = 〈 3^{2}, \log_{2} (2) 〉 \\ ∴ \vec{F} = 〈 9, 1 〉 [∵ \log_{2} (2) = 1] \end{array}$

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Answer 4

Question

Chapter 16, Problem 1CRE

To determine

(a)

The vector assigned to the given point by the given vector field.

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 - 3 (5), 5 - (- 3) 〉 = 〈 - 15, 8 〉$

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 x y, y - x 〉$

Calculation:

Here, $\vec{F} = 〈 x y, y - x 〉$

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 - 3 (5), 5 - (- 3) 〉 = 〈 - 15, 8 〉$

To determine

(b)

The vector assigned to the given point by the given vector field.

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by $\vec{F} = 〈 4, 8 〉$

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 4, 8 〉$

Calculation:

Here, $\vec{F} = 〈 4, 8 〉$

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 4, 8 〉$

To determine

(c)

The vector assigned to the given point by the given vector field.

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 9, 1 〉$

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 3^{x + y}, \log_{2} (x + y) 〉$

Calculation:

Here, $\vec{F} = 〈 3^{x + y}, \log_{2} (x + y) 〉$

Vector assigned to the point P(–3, 5) is given by

$\begin{array}{l} \vec{F} = 〈 3^{- 3 + 5}, \log_{2} (- 3 + 5) 〉 \\ = 〈 3^{2}, \log_{2} (2) 〉 \\ ∴ \vec{F} = 〈 9, 1 〉 [∵ \log_{2} (2) = 1] \end{array}$

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Answer 5

Chapter 16, Problem 1CRE

To determine

(a)

The vector assigned to the given point by the given vector field.

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 - 3 (5), 5 - (- 3) 〉 = 〈 - 15, 8 〉$

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 x y, y - x 〉$

Calculation:

Here, $\vec{F} = 〈 x y, y - x 〉$

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 - 3 (5), 5 - (- 3) 〉 = 〈 - 15, 8 〉$

To determine

(b)

The vector assigned to the given point by the given vector field.

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by $\vec{F} = 〈 4, 8 〉$

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 4, 8 〉$

Calculation:

Here, $\vec{F} = 〈 4, 8 〉$

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 4, 8 〉$

To determine

(c)

The vector assigned to the given point by the given vector field.

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 9, 1 〉$

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 3^{x + y}, \log_{2} (x + y) 〉$

Calculation:

Here, $\vec{F} = 〈 3^{x + y}, \log_{2} (x + y) 〉$

Vector assigned to the point P(–3, 5) is given by

$\begin{array}{l} \vec{F} = 〈 3^{- 3 + 5}, \log_{2} (- 3 + 5) 〉 \\ = 〈 3^{2}, \log_{2} (2) 〉 \\ ∴ \vec{F} = 〈 9, 1 〉 [∵ \log_{2} (2) = 1] \end{array}$

Answer 6

Chapter 16, Problem 1CRE

To determine

(a)

The vector assigned to the given point by the given vector field.

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 - 3 (5), 5 - (- 3) 〉 = 〈 - 15, 8 〉$

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 x y, y - x 〉$

Calculation:

Here, $\vec{F} = 〈 x y, y - x 〉$

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 - 3 (5), 5 - (- 3) 〉 = 〈 - 15, 8 〉$

Answer 7

Chapter 16, Problem 1CRE

To determine

(a)

The vector assigned to the given point by the given vector field.

Answer 8

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 - 3 (5), 5 - (- 3) 〉 = 〈 - 15, 8 〉$

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 x y, y - x 〉$

Calculation:

Here, $\vec{F} = 〈 x y, y - x 〉$

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 - 3 (5), 5 - (- 3) 〉 = 〈 - 15, 8 〉$

Answer 13

To determine

(b)

The vector assigned to the given point by the given vector field.

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by $\vec{F} = 〈 4, 8 〉$

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 4, 8 〉$

Calculation:

Here, $\vec{F} = 〈 4, 8 〉$

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 4, 8 〉$

Answer 14

To determine

(b)

The vector assigned to the given point by the given vector field.

Answer 15

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by $\vec{F} = 〈 4, 8 〉$

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 4, 8 〉$

Calculation:

Here, $\vec{F} = 〈 4, 8 〉$

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 4, 8 〉$

Answer 20

To determine

(c)

The vector assigned to the given point by the given vector field.

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 9, 1 〉$

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 3^{x + y}, \log_{2} (x + y) 〉$

Calculation:

Here, $\vec{F} = 〈 3^{x + y}, \log_{2} (x + y) 〉$

Vector assigned to the point P(–3, 5) is given by

$\begin{array}{l} \vec{F} = 〈 3^{- 3 + 5}, \log_{2} (- 3 + 5) 〉 \\ = 〈 3^{2}, \log_{2} (2) 〉 \\ ∴ \vec{F} = 〈 9, 1 〉 [∵ \log_{2} (2) = 1] \end{array}$

Answer 21

To determine

(c)

The vector assigned to the given point by the given vector field.

Answer 22

Expert Solution

Answer to Problem 1CRE

Solution:

Vector assigned to the point P(–3, 5) is given by

$\vec{F} = 〈 9, 1 〉$

Answer 23

Expert Solution

Answer 24

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given:

The given vector field is $\vec{F} = 〈 3^{x + y}, \log_{2} (x + y) 〉$

Calculation:

Here, $\vec{F} = 〈 3^{x + y}, \log_{2} (x + y) 〉$

Vector assigned to the point P(–3, 5) is given by

$\begin{array}{l} \vec{F} = 〈 3^{- 3 + 5}, \log_{2} (- 3 + 5) 〉 \\ = 〈 3^{2}, \log_{2} (2) 〉 \\ ∴ \vec{F} = 〈 9, 1 〉 [∵ \log_{2} (2) = 1] \end{array}$