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29 , -2 and fy(1, 1) = -4. In our class, we have learned that the partial derivative fæ(1,1) determines a tangent line L1 of graph z = f(x, y) at (1,1, 1). In particular, the line L1 can be described by a system of two equations z – 1 = -2(x – 1), y = 1. f (x, y) at Similarly, fy(1,1) determines one other tangent line L2 of graph z = (1, 1, 1), which can be described by z – 1 = -4(y – 1), | x = 1. a) Write the vector equations of L1 and L2, respectively. Specifically, describe the equation of L1 as = ro + tỉi for some 11, where ro = (1,1, 1). Use a similar argument to describe the equation of L2 as 7= ro+ ti, for some t2. b) Use the previous solution, compute the scalar equation of the plane that contains both L1 and L2.

29 , -2 and fy(1, 1) = -4. In our class, we have learned that the partial derivative fæ(1,1) determines a tangent line L1 of graph z = f(x, y) at (1,1, 1). In particular, the line L1 can be described by a system of two equations z – 1 = -2(x – 1), y = 1. f (x, y) at Similarly, fy(1,1) determines one other tangent line L2 of graph z = (1, 1, 1), which can be described by z – 1 = -4(y – 1), | x = 1. a) Write the vector equations of L1 and L2, respectively. Specifically, describe the equation of L1 as = ro + tỉi for some 11, where ro = (1,1, 1). Use a similar argument to describe the equation of L2 as 7= ro+ ti, for some t2. b) Use the previous solution, compute the scalar equation of the plane that contains both L1 and L2.

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. For function z = f (x, y) where f(x, y) = 4 – x² – 2y², we compute that f#(1, 1) = -2 and fy(1,1) = -4. In our class, we have learned that the partial derivative fæ(1, 1) determines a tangent line L1 of graph z = the line L1 can be described by a system of two equations f(x, y) at (1,1, 1). In particular, z – 1 = -2(x – 1), 1. Similarly, fy(1, 1) determines one other tangent line L2 of graph z = (1, 1, 1), which can be described by f (x, y) at z – 1 = -4(y – 1), x = 1. a) Write the vector equations of L1 and L2, respectively. Specifically, describe the equation of L1 as 7 = ro + tủi for some v1, where ro = (1,1, 1). Use a similar argument to describe the equation of L2 as = ro + ti2 for some 02. b) Use the previous solution, compute the scalar equation of the plane that contains both L1 and L2.
Transcribed Image Text:1. For function z = f (x, y) where f(x, y) = 4 – x² – 2y², we compute that f#(1, 1) = -2 and fy(1,1) = -4. In our class, we have learned that the partial derivative fæ(1, 1) determines a tangent line L1 of graph z = the line L1 can be described by a system of two equations f(x, y) at (1,1, 1). In particular, z – 1 = -2(x – 1), 1. Similarly, fy(1, 1) determines one other tangent line L2 of graph z = (1, 1, 1), which can be described by f (x, y) at z – 1 = -4(y – 1), x = 1. a) Write the vector equations of L1 and L2, respectively. Specifically, describe the equation of L1 as 7 = ro + tủi for some v1, where ro = (1,1, 1). Use a similar argument to describe the equation of L2 as = ro + ti2 for some 02. b) Use the previous solution, compute the scalar equation of the plane that contains both L1 and L2.
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