2) Determine the slope of the tangent line to the function with the given information: a. f(x,y) = arctan(xy) at the point (1, −1), in the direction 2î + 3ĵ. b. f(x, y) = x+6y² y at the point (1,3), going directly away from the origin. c. f(x, y) = −3x + 4y - 10 at the point (4, −3), in the direction 30° clockwise from the negative x-axis. d. f(x, y) = 2x² + xy - y² at the point (4, 2), in the direction toward (7, 1).
2) Determine the slope of the tangent line to the function with the given information: a. f(x,y) = arctan(xy) at the point (1, −1), in the direction 2î + 3ĵ. b. f(x, y) = x+6y² y at the point (1,3), going directly away from the origin. c. f(x, y) = −3x + 4y - 10 at the point (4, −3), in the direction 30° clockwise from the negative x-axis. d. f(x, y) = 2x² + xy - y² at the point (4, 2), in the direction toward (7, 1).
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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Transcribed Image Text:2) Determine the slope of the tangent line to the function with the given information:
a. f(x, y) = arctan(xy) at the point (1,−1), in the direction 2î + 3ĵ.
b. f(x,y) =
x+6y²
y
at the point (1, 3), going directly away from the origin.
c. f(x, y) = −3x + 4y - 10 at the point (4, -3), in the direction 30° clockwise
from the negative x-axis.
d. f(x, y) = 2 - x² + xy - y² at the point (4, 2), in the direction toward (7, 1).
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