Let f(x, y) = 11 - 3x² - 2y² A) fz(x, y) = B) fy(x, y) = C) Find the direction vector for the line tangent to the trace f(x, 1) at x = -2 -6x D) Find the direction vector for the line tangent to the trace f(-2, y) at y = 1 r(t) -4y E)Find parametric equation in R³ for the tangent line to the trace f(x, 1) at x = = - 2. r(t) = F)Find parametric equation in R³ for the tangent line to the trace f(-2, y) at y = 1. z = G) Find the equation of the plane that passes through the point (-2, 1, f(-2, 1)) and whose normal vector is orthogonal to the direction vectors found in (C) and (D)
Let f(x, y) = 11 - 3x² - 2y² A) fz(x, y) = B) fy(x, y) = C) Find the direction vector for the line tangent to the trace f(x, 1) at x = -2 -6x D) Find the direction vector for the line tangent to the trace f(-2, y) at y = 1 r(t) -4y E)Find parametric equation in R³ for the tangent line to the trace f(x, 1) at x = = - 2. r(t) = F)Find parametric equation in R³ for the tangent line to the trace f(-2, y) at y = 1. z = G) Find the equation of the plane that passes through the point (-2, 1, f(-2, 1)) and whose normal vector is orthogonal to the direction vectors found in (C) and (D)
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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please answer c-e
Transcribed Image Text:Let f(x, y) = 11 - 3x² - 2y²
A) fz(x, y) =
B) fy(x, y) =
C) Find the direction vector for the line tangent to the trace f(x, 1) at x = -2
-6x
D) Find the direction vector for the line tangent to the trace f(-2, y) at y = 1
r(t)
-4y
E)Find parametric equation in R³ for the tangent line to the trace f(x, 1) at x =
= - 2.
r(t) =
F)Find parametric equation in R³ for the tangent line to the trace f(-2, y) at y = 1.
z =
G) Find the equation of the plane that passes through the point (-2, 1, f(-2, 1)) and whose normal
vector is orthogonal to the direction vectors found in (C) and (D)
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