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Let f(x, y) = x² + sin(xy), x(t) = 4t+8, and y(t) = 6t² + 4t. The parametric curve c(t) = (x(t), y(t), f(x(t), y(t))) lies on f(x, y). Find the tangent vector to this curve at the surface z = t = 1. Tangent vector = (4 -20 ) , 16

Let f(x, y) = x² + sin(xy), x(t) = 4t+8, and y(t) = 6t² + 4t. The parametric curve c(t) = (x(t), y(t), f(x(t), y(t))) lies on f(x, y). Find the tangent vector to this curve at the surface z = t = 1. Tangent vector = (4 -20 ) , 16

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 33E
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Let f(x, y) = x² + sin(xy), x(t) = 4t+8, and y(t) = 6t² + 4t. The parametric curve c(t) = (x(t), y(t), f(x(t), y(t))) lies on f(x, y). Find the tangent vector to this curve at the surface z = t = 1. Tangent vector = (4 -20 ) , 16
Transcribed Image Text:Let f(x, y) = x² + sin(xy), x(t) = 4t+8, and y(t) = 6t² + 4t. The parametric curve c(t) = (x(t), y(t), f(x(t), y(t))) lies on f(x, y). Find the tangent vector to this curve at the surface z = t = 1. Tangent vector = (4 -20 ) , 16
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