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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
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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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.
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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