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Texts: First, find a location outside somewhere that is not flat (i.e., a hill, street, or something else that is curved and sloped). Take a picture of this location, and if you are able, try to use editing software to indicate the precise point in your picture where you will be doing this activity. Next, use a ruler, yardstick, or another device to try and approximate the change in height in two directions. Pick a direction to call x and estimate the change in the elevation z for an increase of one foot in x. Then, in a direction that is 90 degrees counterclockwise, representing y, do the same thing. Explain the significance of the two values you determined, and then use them to find an approximate equation of a tangent plane at this point (you may assume your starting point is the origin for convenience). Finally, say that you were going to walk in the <1,1>-direction; would your path be initially ascending, descending, or stay at the same elevation? Use your previous answers to explain your reasoning. I need help with this assignment, please.

          Texts: First, find a location outside somewhere that is not flat (i.e., a hill, street, or something else that is curved and sloped). Take a picture of this location, and if you are able, try to use editing software to indicate the precise point in your picture where you will be doing this activity. 

Next, use a ruler, yardstick, or another device to try and approximate the change in height in two directions. Pick a direction to call x and estimate the change in the elevation z for an increase of one foot in x. Then, in a direction that is 90 degrees counterclockwise, representing y, do the same thing. 

Explain the significance of the two values you determined, and then use them to find an approximate equation of a tangent plane at this point (you may assume your starting point is the origin for convenience). 

Finally, say that you were going to walk in the <1,1>-direction; would your path be initially ascending, descending, or stay at the same elevation? Use your previous answers to explain your reasoning. 

I need help with this assignment, please.

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Added by Brianna A.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Akash M

07/19/2023

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Use editing software to indicate the precise point where you will be doing this activity. Show more…

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Texts: First, find a location outside somewhere that is not flat (i.e., a hill, street, or something else that is curved and sloped). Take a picture of this location, and if you are able, try to use editing software to indicate the precise point in your picture where you will be doing this activity. Next, use a ruler, yardstick, or another device to try and approximate the change in height in two directions. Pick a direction to call x and estimate the change in the elevation z for an increase of one foot in x. Then, in a direction that is 90 degrees counterclockwise, representing y, do the same thing. Explain the significance of the two values you determined, and then use them to find an approximate equation of a tangent plane at this point (you may assume your starting point is the origin for convenience). Finally, say that you were going to walk in the <1,1>-direction; would your path be initially ascending, descending, or stay at the same elevation? Use your previous answers to explain your reasoning. I need help with this assignment, please.

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Transcript

00:08 Process of understanding and using partial derivatives to predict and interact with the world around you are process of understanding and using partial derivatives.

00:37 First is to find a location.

00:40 First what we need is to find a location.

00:49 To choose a location outside with a curved and sloped surface such as a hill or a sloping street.

00:54 Second is to take a picture.

01:01 So take a picture of the location and if possible indicate the precise point where you will be conducting the activity under using editing software.

01:10 Then is approximate change in the height.

01:14 Approximate change in the height.

01:26 So using a ruler or a yardstick measure the change in height in two perpendicular direction at the chosen point.

01:32 Let's follow the direction you move the ruler in the x direction and the change in height for one foot in the x direction as z divided by x.

01:42 Then move the ruler 90 degrees counterclockwise which we call the y direction and measure the change in the height for one foot in the y direction.

01:57 So significance and tangent plane.

02:04 Significant and tangent plane.

02:18 The values z divided by x and z represented the rates of change of elevation in the x and y direction respectively.

02:26 These values are partial derivates of the elevation function at the chosen point.

02:30 They indicate how much elevation changes with respect to each direction.

02:35 The tangent plane at the point is given by the equation z minus equals to x into x minus.

02:56 Excuse me...

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