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1. Given the equation: 1 1 + -= 1 x y (1) (a) Find by applying implicit differentiation in eq (1). dx (b) Solve eq (1) explicitly for y as a function of x. dy (c) Differentiate your result from (b) to find in terms of only x. dx (d) To check that your two solutions are consistent, substitute your expression for y from (b) into your solution for from dy dx dy part (a). The result should be your answer for from (c). dx (e) Use your formula for dy to find all the points on the graph of the hyperbola at which the slope is -4. dx 2. The graph shown below is that of the bifolium: ~ N 7 X 2 + = 1 4

1. Given the equation: 1 1 + -= 1 x y (1) (a) Find by applying implicit differentiation in eq (1). dx (b) Solve eq (1) explicitly for y as a function of x. dy (c) Differentiate your result from (b) to find in terms of only x. dx (d) To check that your two solutions are consistent, substitute your expression for y from (b) into your solution for from dy dx dy part (a). The result should be your answer for from (c). dx (e) Use your formula for dy to find all the points on the graph of the hyperbola at which the slope is -4. dx 2. The graph shown below is that of the bifolium: ~ N 7 X 2 + = 1 4

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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1. Given the equation: 1 1 + -= 1 x y (1) (a) Find by applying implicit differentiation in eq (1). dx (b) Solve eq (1) explicitly for y as a function of x. dy (c) Differentiate your result from (b) to find in terms of only x. dx (d) To check that your two solutions are consistent, substitute your expression for y from (b) into your solution for from dy dx dy part (a). The result should be your answer for from (c). dx (e) Use your formula for dy to find all the points on the graph of the hyperbola at which the slope is -4. dx 2. The graph shown below is that of the bifolium: ~ N 7 X 2 + = 1 4
Transcribed Image Text:1. Given the equation: 1 1 + -= 1 x y (1) (a) Find by applying implicit differentiation in eq (1). dx (b) Solve eq (1) explicitly for y as a function of x. dy (c) Differentiate your result from (b) to find in terms of only x. dx (d) To check that your two solutions are consistent, substitute your expression for y from (b) into your solution for from dy dx dy part (a). The result should be your answer for from (c). dx (e) Use your formula for dy to find all the points on the graph of the hyperbola at which the slope is -4. dx 2. The graph shown below is that of the bifolium: ~ N 7 X 2 + = 1 4
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