Let f(x, y)=sin(xy-x-3y+3). (i) Determine the domain and range of f. (ii) Factor the argument of the sin function. Does this factored form give any hints about the appear- ance of the surface z = f(x, y)? (iii) Find a relationship for the x cross-sections by letting x = k, k = R. Then, • tabulate the relationships for k = 0, 1, ..., 6; • sketch the relationships for k = 3, 4, 5, 6 on the interval y ≤ [1 − ˜, 1±Ã] ; and ⚫ with respect to the cross-sections for k = 4, 5, 6, describe the cross-sections for k = 0, 1, 2. (iv) Find a relationship for the level curves / contours by letting z = m, m = R. You must recognise the periodic nature of f and ensure the relationship accounts for it. (v) Sketch the contours m = 0 on the interval x€ (-1,7], y ≤ [−3, 5] . (vi) Which of the surfaces below is a graph of this function?
Let f(x, y)=sin(xy-x-3y+3). (i) Determine the domain and range of f. (ii) Factor the argument of the sin function. Does this factored form give any hints about the appear- ance of the surface z = f(x, y)? (iii) Find a relationship for the x cross-sections by letting x = k, k = R. Then, • tabulate the relationships for k = 0, 1, ..., 6; • sketch the relationships for k = 3, 4, 5, 6 on the interval y ≤ [1 − ˜, 1±Ã] ; and ⚫ with respect to the cross-sections for k = 4, 5, 6, describe the cross-sections for k = 0, 1, 2. (iv) Find a relationship for the level curves / contours by letting z = m, m = R. You must recognise the periodic nature of f and ensure the relationship accounts for it. (v) Sketch the contours m = 0 on the interval x€ (-1,7], y ≤ [−3, 5] . (vi) Which of the surfaces below is a graph of this function?
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.6: Parametric Equations
Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...
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please answer parts iv), v) and vi) of this question, i have attached the first the given answers to the first three parts of the question for assistance
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