Question 2. Consider the parametrized surface S: F(u, v) = (u sec v, u tan v, u?) (-o < u < 00, -1/2 < v < 7/2) and the parametrized curve C: F(t) = (tan t, sinttant, sin? t) (-7/2 < t < n/2). %3D %3D (a) Verify that S is the hyperbolic paraboloid r² – y² = z and that C lies completely in S. (b) Find a nonzero vector ī perpendicular to the tangent vector to C at (1, ,) such that i is also tangent to S at (1, ). (c) What is the rate of change of the function f(r, y, z) = 2ry+z² along C at the point (1, 2,)? df In other words, what is dt |(1,41)
Question 2. Consider the parametrized surface S: F(u, v) = (u sec v, u tan v, u?) (-o < u < 00, -1/2 < v < 7/2) and the parametrized curve C: F(t) = (tan t, sinttant, sin? t) (-7/2 < t < n/2). %3D %3D (a) Verify that S is the hyperbolic paraboloid r² – y² = z and that C lies completely in S. (b) Find a nonzero vector ī perpendicular to the tangent vector to C at (1, ,) such that i is also tangent to S at (1, ). (c) What is the rate of change of the function f(r, y, z) = 2ry+z² along C at the point (1, 2,)? df In other words, what is dt |(1,41)
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:Question 2. Consider the parametrized surface S: F(u, v) = (u sec v, u tan v, u²) (-∞ < u <∞, –T/2 <
v < 7/2) and the parametrized curve C: 7(t)
(tan t, sin t tan t, sin? t) (-1/2 < t < 7/2).
(a)
Verify that S is the hyperbolic paraboloid æ² – y?
= z and that C lies completely in S.
(b)
Find a nonzero vector ī perpendicular to the tangent vector to C at
(1, 2, 글) such that 히
(号)
is also tangent to S at
(c)
What is the rate of change of the function f(x, y, z) = 2ry+z² along C at the point (1, ,)?
df
In other words, what is
dt (1,4)
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