5) Determine the slope of the tangent line to the function with the given information: a. f(x, y) = sin(xy) in the direction 2î - 3ĵ, at the point (π, -1). 3+x² b. f(x, y) = going directly away from the origin, at the point (4, -1). y² c. f(x, y) = -6x + 2y + 3 in the direction 30° counter-clockwise from the negative y-axis, at the point (-2,2).
5) Determine the slope of the tangent line to the function with the given information: a. f(x, y) = sin(xy) in the direction 2î - 3ĵ, at the point (π, -1). 3+x² b. f(x, y) = going directly away from the origin, at the point (4, -1). y² c. f(x, y) = -6x + 2y + 3 in the direction 30° counter-clockwise from the negative y-axis, at the point (-2,2).
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:5) Determine the slope of the tangent line to the function with the given information:
a. f(x, y) = sin(xy) in the direction 2î - 3ĵ, at the point (, -1).
b. f(x, y) =
3+x²
y²
going directly away from the origin, at the point (4,−1).
c. f(x, y) = -6x + 2y + 3 in the direction 30° counter-clockwise from the
negative y-axis, at the point (-2,2).
d. f(x, y) = x³y² + √3x − y in the direction toward (0,5), at the point (3, 1).
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