PLEASE ANSWER ASAP 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, ,)?dfIn other words, what isdt (1,4)

The general form of the parametric equation of the curve in three dimensional space is given by…

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)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 17T

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