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Use the following applet to answer the questions that follow (clickable link) →→→ Contour Plot The given function should be f(x, y) = x² - y². Do not change this function. (a) Determine Vf(x, y). (b) Calculate Vƒ(-2,-2). (c) Find the unit vector in the direction of fastest increase at the point (-2,-2). How do you know it is the direction of fastest increase?

Use the following applet to answer the questions that follow (clickable link) →→→ Contour Plot The given function should be f(x, y) = x² - y². Do not change this function. (a) Determine Vf(x, y). (b) Calculate Vƒ(-2,-2). (c) Find the unit vector in the direction of fastest increase at the point (-2,-2). How do you know it is the direction of fastest increase?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use the following applet to answer the questions that follow (clickable link) → Contour Plot The given function should be f(x, y) = x² - y². Do not change this function. (a) Determine Vf(x, y). (b) Calculate Vƒ(-2,-2). (c) Find the unit vector in the direction of fastest increase at the point (-2,-2). How do you know it is the direction of fastest increase? this unit vector on the contour map and provide that sketch in your answer below. (d) Sketch (e) Let v = (3,2). Calculate Dvƒ(2, 1). (f) Sketch this on the contour map. (g) Provide an interpretation of your answers to the previous two parts. In other words, explain what the answers to (e) and (f) mean.
Transcribed Image Text:Use the following applet to answer the questions that follow (clickable link) → Contour Plot The given function should be f(x, y) = x² - y². Do not change this function. (a) Determine Vf(x, y). (b) Calculate Vƒ(-2,-2). (c) Find the unit vector in the direction of fastest increase at the point (-2,-2). How do you know it is the direction of fastest increase? this unit vector on the contour map and provide that sketch in your answer below. (d) Sketch (e) Let v = (3,2). Calculate Dvƒ(2, 1). (f) Sketch this on the contour map. (g) Provide an interpretation of your answers to the previous two parts. In other words, explain what the answers to (e) and (f) mean.
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