Continuity | Continuous | Whether xsin(1/x) is continuous at 0 or not

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x Sin(1/x) is continuous at x=0 but not differentiable x Sin(1/x) is continuous at x=0 but not differentiable
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Show that the function f defined by f(x) = xsin(1/x) and 0 when x=0 is continuous at x=0. Show that the function f defined by f(x) = xsin(1/x) and 0 when x=0 is continuous at x=0.
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Double limit exist but repeated limits do not exist at origin for , f(x,y)=xSin(1/y)+ySin(1/x) Double limit exist but repeated limits do not exist at origin for , f(x,y)=xSin(1/y)+ySin(1/x)