а. Propose values for A, B,C,D, and E such that it will give THREE (3) extreme seabed profiles M(x,y). Verify the extrema with the derivative test.

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Chapter2: Second-order Linear Odes
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1. A geoscientist is logging the profile of seabed to discover the hydrocarbon. The map can be represented by General Mathematical Model as in the given picture.

(*The questions are uploaded in the picture format so there are a total of 4 subquestions where each question is related to the another. Therefore to answer the next question you have to answer the first question correctly and then only you can move on to the next question. Thank you.) (*The given equation for the solution is in the picture .

а.
Propose values for A, B,C,D, and E such that it will give THREE (3) extreme
seabed profiles M(x,y). Verify the extrema with the derivative test.
b.
If the gradient of the seabed in x and y axes is changing over the time t,
constructs the functions x(t) and y(t) to show THREE (3) displacements of
seabed M over the time t. Sketch the graphs.
с.
Find the directional derivatives of the seabed profiles obtained in Q1(a)
subjected to Q1(b).
d.
From the results in Q1(a), Q1(b) and Q1(c), suggest a best place to land an
oil rig. Justify your answer.
Transcribed Image Text:а. Propose values for A, B,C,D, and E such that it will give THREE (3) extreme seabed profiles M(x,y). Verify the extrema with the derivative test. b. If the gradient of the seabed in x and y axes is changing over the time t, constructs the functions x(t) and y(t) to show THREE (3) displacements of seabed M over the time t. Sketch the graphs. с. Find the directional derivatives of the seabed profiles obtained in Q1(a) subjected to Q1(b). d. From the results in Q1(a), Q1(b) and Q1(c), suggest a best place to land an oil rig. Justify your answer.
M(x,y) = Ax³ + By³ – Cx – Dy + E
|
Transcribed Image Text:M(x,y) = Ax³ + By³ – Cx – Dy + E |
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