Let the 𝒇(𝒙, 𝒚) = { 𝒄𝒐𝒔𝒚. 𝒔𝒊𝒏𝒙, 𝒙 ≠ 𝟎 𝒄𝒐𝒔𝒚, 𝒙 = 𝟎 }. Is 𝒇(𝒙, 𝒚) continues at (𝟎, 𝟎)? Is 𝒇(𝒙, 𝒚) continues everywhere?
The function has the form: "f(x,y)=cos\\,y\\,\\,sin\\,x,\\,\\,x\\neq0" and "f(x,y)=cos\\,y,\\,\\, x=0". Set "y=0"Then, "f(x,y)=1" at "x=0,y=0" and "f(x,y)=sin\\,x" if "x\\neq0". But "sin\\,x" approaches 0 as "x" tends to .Thus, the function is not continuous at "x=0,y=0."
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