Let f(x, y) = x³ + y' (a) Compute f(x, y) along an arbitrary line through the origin. Use parametric equa- lim (x,y)→(0,0) tions to represent your arbitrary line. (b) Now use a nonlinear path passing through (0,0) to show lim (x,y)→(0,0) above describe your path using parametric equations of the form f (x, y) does not exist. As f1(t), X = y = f2(t).

Let f(x, y) = x³ + y' (a) Compute f(x, y) along an arbitrary line through the origin. Use parametric equa- lim (x,y)→(0,0) tions to represent your arbitrary line. (b) Now use a nonlinear path passing through (0,0) to show lim (x,y)→(0,0) above describe your path using parametric equations of the form f (x, y) does not exist. As f1(t), X = y = f2(t).

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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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

3. Let
f(x, y) :
x5 + y7"
(a) Compute
f (x, y) along an arbitrary line through the origin. Use parametric equa-
lim
(x,y)→(0,0)
tions to represent your arbitrary line.
(b) Now use a nonlinear path passing through (0,0) to show
f (x, y) does not exist. As
lim
(x,y)→(0,0)
above describe your path using parametric equations of the form
x = f1(t),
y = f2(t).

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