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Consider the scalar functions 1(2,9) = arctan(). %3D (2, y, =) = sin(z)e In(2), and the vector field F= (e, In(zy), e=), and the statements i)1(z, y) is harmonic for z>0 i) Voz(z, y) = (cos(z)e® In(2), sin(z)e In(2), sin(z)e"=) im V -F = e ++ e iv) 2(z, y) is harmonic for all :> 0 V-F= (e", , rye). Which one of the following statements is true? O Only statement iv) is true O Only statement i) is true Statements i) and v) are true Only statement v) is true None of these options are true Statements i) and v) are true Only statement i) is true O Statements and iv) are true Oinly statement is true

Consider the scalar functions 1(2,9) = arctan(). %3D (2, y, =) = sin(z)e In(2), and the vector field F= (e, In(zy), e=), and the statements i)1(z, y) is harmonic for z>0 i) Voz(z, y) = (cos(z)e® In(2), sin(z)e In(2), sin(z)e"=) im V -F = e ++ e iv) 2(z, y) is harmonic for all :> 0 V-F= (e", , rye). Which one of the following statements is true? O Only statement iv) is true O Only statement i) is true Statements i) and v) are true Only statement v) is true None of these options are true Statements i) and v) are true Only statement i) is true O Statements and iv) are true Oinly statement is true

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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Consider the scalar functions 1(2,y) = arctan(). 2(z, y, 2) = sin(z) In(2), and the vector field F= (e, In(zy), ey=), and the statements i)(z, y) is harmonic for z >0 i) Vo2(z, y) = (cos(z)e® In(2), sin(z)e In(2), sin(z)e":) im V F= e ++ e eyz Mos(z, y) is harmonic for all :>0 V-F= (e", , zye). Which one of thefollowing statements is true? O Only statement iv) is true O Only statement i) is true Statements li) and v) are true Only statement v) is true None of these options are true Statements i) and vi are true Only statement i is true Statements andivaretrue 0Onystatement istrue
Transcribed Image Text:Consider the scalar functions 1(2,y) = arctan(). 2(z, y, 2) = sin(z) In(2), and the vector field F= (e, In(zy), ey=), and the statements i)(z, y) is harmonic for z >0 i) Vo2(z, y) = (cos(z)e® In(2), sin(z)e In(2), sin(z)e":) im V F= e ++ e eyz Mos(z, y) is harmonic for all :>0 V-F= (e", , zye). Which one of thefollowing statements is true? O Only statement iv) is true O Only statement i) is true Statements li) and v) are true Only statement v) is true None of these options are true Statements i) and vi are true Only statement i is true Statements andivaretrue 0Onystatement istrue
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