a)Sketch some level curves of the function f(x,y)=(x^2+y^2)/x b) Verify Clairaut's theorem for f(x,y) = arctan (y/x). ` `

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aruv | High School Teacher | (Level 2) Valedictorian

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Verify Clairaut's theorem for f(x,y) = arctan (y/x).

A function f is defined at a point (a,b) in its domain of definition. If

`f_(xy) and f_(yx)` are continuous in domain of definition of f, then



`f(x,y)=tan^(-1)(y/x)`   (i)

Differentiate (i) partially  with respect to x and y respectively.

`(delf(x,y))/(delx )=f_x=1/(1+(y/x)^2)del/(delx)(y/x)`



`(delf_x)/(del y)=(del(-y/(x^2+y^2)))/(dely)`











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