Answer & Explanation:I do not want the steps just i want the answers. please be clear about the answers and the number of the questions.

sec._14.5__gradient_and_directional_derivatives___math_2163__section_61998__fall_2019___webassign.pdf

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Sec. 14.5: Gradient and Directional Derivatives – MATH 2163, section 61998, Fall 2019 | WebAssign

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MATH 2163, section 61998, Fall 2019

INSTRUCTOR

Sec. 14.5: Gradient and Directional Derivatives

(Calculus3Homework)

Ning Ju

Northern Oklahoma

College

Current Score

QUESTION

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

POINTS

1/1

0/2

–/1

0/1

–/1

–/1

–/1

–/1

–/1

–/1

–/1

–/1

–/2

–/1

–/1

–/2

TOTAL SCORE

1/19

5.3%

Due Date

DECEMBER 14

11:32 PM CST

Assignment Submission & Scoring

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each

question part only changes if you submit or change the answer.

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1/8

11/16/2019

Sec. 14.5: Gradient and Directional Derivatives – MATH 2163, section 61998, Fall 2019 | WebAssign

Assignment Scoring

Your best submission for each question part is used for your score.

1.

1/1 points

Previous Answers

RogaCalcET3 14.5.003.

My Notes

The figure below shows the level curves of a function f(x, y) and a path r(t), traversed in the direction

d

indicated. State whether the derivative

f(r(t)) is positive, negative, or zero at points A-D.

dt

At point A the derivative is zero

.

At point B the derivative is negative

.

At point C the derivative is positive

.

At point D the derivative is zero

.

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2.

Sec. 14.5: Gradient and Directional Derivatives – MATH 2163, section 61998, Fall 2019 | WebAssign

0/2 points

Previous Answers

RogaCalcET3 14.5.002.

My Notes

Let f(x, y) = 4exy and r(t) = (t3, 4 + t).

1. Calculate ∇f.

∇f =

2. Calculate r'(t).

r'(t) =

3t2,5

3. Use the Chain Rule for Paths to calculate

d

f(r(t)) =

dt

d

f(r(t)).

dt

4. Write out the composite f(r(t)) as a function of t.

f(r(t)) =

5. Differentiate f(r(t)).

d

f(r(t)) =

dt

Check that the results of (3) and (5) agree.

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Sec. 14.5: Gradient and Directional Derivatives – MATH 2163, section 61998, Fall 2019 | WebAssign

–/1 points

3.

RogaCalcET3 14.5.005.

My Notes

Calculate the gradient.

f(x, y) = cos(x8 + y)

∇f =

0/1 points

4.

Previous Answers

RogaCalcET3 14.5.007.

My Notes

Calculate the gradient.

h(x, y, z) = xyz8

∇f =

8xyz7

5.

–/1 points

RogaCalcET3 14.5.010.

Use the Chain Rule to calculate

My Notes

d

f(r(t)).

dt

f(x, y) = 2x − 7y, r(t) = t4, t5 , t = 3

d

f(r(t)) =

dt

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6.

Sec. 14.5: Gradient and Directional Derivatives – MATH 2163, section 61998, Fall 2019 | WebAssign

–/1 points

RogaCalcET3 14.5.011.

Use the Chain Rule to calculate

My Notes

d

f(r(t)).

dt

f(x, y) = x3 − 5xy, r(t) = (cos(3t), sin(3t)), t = 0

d

f(r(t)) =

dt

7.

–/1 points

RogaCalcET3 14.5.015.

Use the Chain Rule to calculate

My Notes

d

f(r(t)).

dt

f(x, y) = 5x − 4xy, r(t) = (t2, t2 − 2t), t = 2

d

f(r(t)) =

dt

8.

–/1 points

RogaCalcET3 14.5.018.

Use the Chain Rule to calculate

My Notes

d

f(c(t)).

dt

f(x, y, z) = x8y7e4z, c(t) = (t2, t3, t − 1), t = 1

d

f(c(t)) =

dt

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Sec. 14.5: Gradient and Directional Derivatives – MATH 2163, section 61998, Fall 2019 | WebAssign

–/1 points

9.

RogaCalcET3 14.5.021.

My Notes

Calculate the directional derivative in the direction of v at the given point. Remember to normalize the

direction vector.

f(x, y) = x2 + y3,

v = 2, 5 ,

P = (5, 2)

Du f(P) =

10.

–/1 points

RogaCalcET3 14.5.025.Tutorial.SA.

My Notes

This question has several parts that must be completed sequentially. If you skip a part of the question, you

will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

Tutorial Exercise

Calculate the directional derivative in the direction of v at the given point. Remember to normalize the

1

direction vector or use Duf(P) =

∇fP · v.

v

f(x, y) = tan−1(xy),

11.

–/1 points

v = 1, 1 ,

P = (6, 3)

RogaCalcET3 14.5.028.

My Notes

Calculate the directional derivative in the direction of v at the given point. Remember to normalize the

direction vector.

f(x, y, z) = z2 − xy2,

v = −1, 2, 2 ,

P = (4, 5, 8)

Du f(4, 5, 8) =

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12.

Sec. 14.5: Gradient and Directional Derivatives – MATH 2163, section 61998, Fall 2019 | WebAssign

–/1 points

RogaCalcET3 14.5.032.

My Notes

Let f(x, y, z) = xy + z4, P = (8, 6, 1). Calculate the directional derivative in the direction pointing to the

origin. Remember to normalize the direction vector.

Du f(8, 6, 1) =

13.

–/2 points

RogaCalcET3 14.5.038.

My Notes

2

Let f(x, y) = xex − y and P = (9, 81).

(a) Calculate

∇fP .

∇fP =

(b) Find the rate of change of f in the direction ∇fP.

(c) Find the rate of change of f in the direction of a vector making an angle of 45° with ∇fP.

14.

–/1 points

RogaCalcET3 14.5.041.

My Notes

Find a vector normal to the surface x2 + y2 − z2 = 40 at P = (4, 5, 1).

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15.

Sec. 14.5: Gradient and Directional Derivatives – MATH 2163, section 61998, Fall 2019 | WebAssign

–/1 points

RogaCalcET3 14.5.044.

My Notes

Find an equation of the tangent plane to the surface at the given point.

5×2 + 4y2 + 3z2 = 136,

16.

–/2 points

P = (3, 2, 5)

RogaCalcET3 14.5.046.

My Notes

Find an equation of the tangent plane to the surface at the given point.

x2 + 2z2ey − x = 41,

P=

3, 4,

4

e

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