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7. (a) The function f is given by f(x,y) = c²-/ª In(x² + y²). Find the partial derivatives Show that, for z, y 0, 10f 2 Or of Эх and 1df of 4f(x, y).

7. (a) The function f is given by f(x,y) = c²-/ª In(x² + y²). Find the partial derivatives Show that, for z, y 0, 10f 2 Or of Эх and 1df of 4f(x, y).

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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Q↑↓ 4 of 5 7. (a) The function f is given by f(x, y) Find the partial derivatives rassessment |_c¹ª-"ª În(x² + y²). Of and Show that, for x, y 0, 1af 2 OT у ду Dy + Automatic Zoom 4f(z,1). (b) A firm is the only supplier of two goods, X and Y and the demand equations for these goods are 4x PX 200 and 2y py| 152. where px and py are the prices of X and Y and 2 andy are the quantities of X and Y (respectively). The firm's joint total cost function is C(r, y) — 6x² + 4xy + 4y² + 20. Find an expression, in terms of # and y, for the firm's profit function. Determine the values of x and y that maximise the profit. What are the corresponding prices! Page 4 of 5 ✔
Transcribed Image Text:Q↑↓ 4 of 5 7. (a) The function f is given by f(x, y) Find the partial derivatives rassessment |_c¹ª-"ª În(x² + y²). Of and Show that, for x, y 0, 1af 2 OT у ду Dy + Automatic Zoom 4f(z,1). (b) A firm is the only supplier of two goods, X and Y and the demand equations for these goods are 4x PX 200 and 2y py| 152. where px and py are the prices of X and Y and 2 andy are the quantities of X and Y (respectively). The firm's joint total cost function is C(r, y) — 6x² + 4xy + 4y² + 20. Find an expression, in terms of # and y, for the firm's profit function. Determine the values of x and y that maximise the profit. What are the corresponding prices! Page 4 of 5 ✔
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