A normal line to a surface S at a point (x, y, z) E S is a line perpendicular to the tangent plane to S at(x, y, z).a) Find the second intersection point between the normal line to the level surface F(x, y, z) = x² +1 at the point (1, –1, –1) and the same surface (normal line intersects the level surface at 2 points).b) Compute the second order directional derivativeDif(x, y)for f(x, y) = sin(r) sin(y), ū = (v3/2,1/2) at (x, y) = (T/2,0).

Answered: Image /qna-images/answer/896de66c-79ef-4929-a981-c7e19b74faf2.jpg

A normal line to a surface S at a point (x, y, z) E S is a line perpendicular to the tangent plane to S at (x, Y, z). a) Find the second intersection point between the normal line to the level surface F(x, y, z) = x² + y? - z2 = 1 at the point (1, –1,-1) and the same surface (normal line intersects the level surface at 2 points). b) Compute the second order directional derivative Df(x, y) for f(x, y) = sin(x) sin(y), ū = :(V3/2,1/2) at (x, y) = (1/2,0).

A normal line to a surface S at a point (x, y, z) E S is a line perpendicular to the tangent plane to S at (x, Y, z). a) Find the second intersection point between the normal line to the level surface F(x, y, z) = x² + y? - z2 = 1 at the point (1, –1,-1) and the same surface (normal line intersects the level surface at 2 points). b) Compute the second order directional derivative Df(x, y) for f(x, y) = sin(x) sin(y), ū = :(V3/2,1/2) at (x, y) = (1/2,0).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.2: Properties Of Division

Problem 53E

See similar textbooks