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Partial derivative using the definition

  • Thread starter U.Renko
  • Start date
  • #1
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Homework Statement



So I'm supposed to find the partial derivatives and calculate them at point (0,2) using the definition


Homework Equations



[itex] f(x,y) = x^2y\sin(1/x) [/itex] IF x ≠ 0
[itex] f(x,y) = 0 [/itex] IF x = 0



The Attempt at a Solution



[itex]\frac{lim_{\Delta_x\rightarrow0} = (x + \Delta_x)^2y\sin(1/x+\Delta_x) - x^2y\sin(1/x)}{\Delta_x}[/itex]



the thing is, I'm not very sure how to solve
[itex] \lim_{\Delta_x\rightarrow0} \sin(1/x+\Delta_x) [/itex]

and if I just consider it the same as sin(1/x)
things get messed up

also this is my first time using LaTex.
Hope I did fine.
 

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