3xy x² +4x° Given the function f(x, y) = i) Determine whether or not lim (x,y)(0,0) f (x, y) exist, by considering the limits along any straight line y= mx and the curve x = y'. ii) Is the function f(x, y) continuous at (0,0)? Justify your answer.
3xy x² +4x° Given the function f(x, y) = i) Determine whether or not lim (x,y)(0,0) f (x, y) exist, by considering the limits along any straight line y= mx and the curve x = y'. ii) Is the function f(x, y) continuous at (0,0)? Justify your answer.
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:3xy3
x' +4x°
Determine whether or not
Q1
(а)
Given the function f(x, y) =-
(i)
lim
f (x, y) exist, by considering the limits
(х, у)-(0,0)
= y'.
along any straight line y =mx and the curve x =
Is the function f(x, y) continuous at (0,0)? Justify your answer.
(ii)
dz
dz
(b)
Use chain rule to find
and
if given that z
= e*y – y* +2x, x= 3p – In q and
y =1+q° – sin(qr) .
(c)
Use cylindrical coordinates, (r,0, z) to compute the volume of the solid that is
bounded above by sphere r² +z = 8 and below by cone z=r.
(d)
Evaluate
I[(* + y* + z° }³ av
where B is the unit ball B
= {(x, y, z) : x² + y² + z² <1}. Use spherical coordinates.
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