= 1. (a) Compute the directional derivative of f(x, z)= = x²z+xz³ at the point (x,z) (-2,4) in the direction û = (3, 1)/√/10. = (b) Find the equation of the tangent plane to the surface z = f(x, y) = x² - y², at the point (1, 2, -3), in the form ax+by+cz = d. - (c) The function f(x, y, z) = x² + 3xy + 2yz + y² − z² – 11 = 0 defines an implicit function <= z(x, y). Show that the point (x, y, z) = (1, 2, 0) yields f = 0. Find az/ax, az/ay and evaluate them at the given point (x, y, z) = (1, 2,0).
= 1. (a) Compute the directional derivative of f(x, z)= = x²z+xz³ at the point (x,z) (-2,4) in the direction û = (3, 1)/√/10. = (b) Find the equation of the tangent plane to the surface z = f(x, y) = x² - y², at the point (1, 2, -3), in the form ax+by+cz = d. - (c) The function f(x, y, z) = x² + 3xy + 2yz + y² − z² – 11 = 0 defines an implicit function <= z(x, y). Show that the point (x, y, z) = (1, 2, 0) yields f = 0. Find az/ax, az/ay and evaluate them at the given point (x, y, z) = (1, 2,0).
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:1. (a) Compute the directional derivative of f(x, z) = x²z+xz³ at the point (x, z) =
(-2, 4) in the direction û = (3, 1)/√/10.
(b) Find the equation of the tangent plane to the surface z = f (x, y) x² - y², at
the point (1, 2, -3), in the form ax +by+cz = d.
=
(c) The function f(x, y, z) = x² + 3xy + 2yz + y² − z² – 11 = 0 defines an implicit
function z = z(x, y). Show that the point (x, y, z) = (1, 2, 0) yields f = 0. Find
az/ax, dz/dy and evaluate them at the given point (x, y, z) = (1, 2, 0).
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