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Question 8 z = sin(x + y), x = u² + v², y = 2uv, find the partial derivative of z with respect to u? (a) -(2u + 2v)cos (x + y) (b) (2u + 2v)cos (x + y) (c) (2u + 2v)cos (x) (d) None of these

Question 8 z = sin(x + y), x = u² + v², y = 2uv, find the partial derivative of z with respect to u? (a) -(2u + 2v)cos (x + y) (b) (2u + 2v)cos (x + y) (c) (2u + 2v)cos (x) (d) None of these

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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Question 8 z = sin(x + y), x = u² + v², y = 2uv, find the partial derivative of z with respect to u? (a) (2u + 2v)cos (x + y) (b) (2u + 2v)cos (x + y) Question 9 Given that z = 5xy - 4x² - y² - 2x - y + 5 has a stationary point (1,2). This point is a/an? (a) Maximum point (b) Minimum point Question 10 If z = x³ - 3x + xy² then (0, -1) is a? Question 11 (a) Maximum point (c) Saddle point (b) Minimum point (d) None of these Choose the appropriate method in each case from question 11 to Question 15. (a) Separating the Variable (b) Homogeneous Equation (c) Integrating Factor (d) Bernoulli's Equation y + (x² - 4x) = 0 dx Question 12 (1-x²) ¹=1+xy dy Question 13 (x² - 2xy + 5y²) = (x² + 2xy + y²) dx Question 14 dx -ycotx = y²sec²x Question 15 dy (c) (2u + 2v)cos (x) (d) None of these xy-(1+x)√√y²-1=0 dx (c) Saddle point (d) None of these
Transcribed Image Text:Question 8 z = sin(x + y), x = u² + v², y = 2uv, find the partial derivative of z with respect to u? (a) (2u + 2v)cos (x + y) (b) (2u + 2v)cos (x + y) Question 9 Given that z = 5xy - 4x² - y² - 2x - y + 5 has a stationary point (1,2). This point is a/an? (a) Maximum point (b) Minimum point Question 10 If z = x³ - 3x + xy² then (0, -1) is a? Question 11 (a) Maximum point (c) Saddle point (b) Minimum point (d) None of these Choose the appropriate method in each case from question 11 to Question 15. (a) Separating the Variable (b) Homogeneous Equation (c) Integrating Factor (d) Bernoulli's Equation y + (x² - 4x) = 0 dx Question 12 (1-x²) ¹=1+xy dy Question 13 (x² - 2xy + 5y²) = (x² + 2xy + y²) dx Question 14 dx -ycotx = y²sec²x Question 15 dy (c) (2u + 2v)cos (x) (d) None of these xy-(1+x)√√y²-1=0 dx (c) Saddle point (d) None of these
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