Q5·Section A (Section A)·5 of 15Continuity and partial derivatives at a point for an oscillating function of two variablesLet f(x,y)={x2+y2 sin(1x2+y2),(x,y)≠(0,0), 0,(x,y)=(0,0).f(x,y)=\begin{cases}\sqrt{x^2+y^2}\,\sin\left(\dfrac1{\sqrt{x^2+y^2}}\right), & (x,y)\ne(0,0),\ 0, & (x,y)=(0,0).\end{cases}f(x,y)={x2+y2sin(x2+y21),(x,y)=(0,0), 0,(x,y)=(0,0). Then at the point (0,0)(0,0)(0,0), OptionsAfff is continuous and ∂f∂x\frac{\partial f}{\partial x}∂x∂f and ∂f∂y\frac{\partial f}{\partial y}∂y∂f existBfff is continuous and ∂f∂x\frac{\partial f}{\partial x}∂x∂f and ∂f∂y\frac{\partial f}{\partial y}∂y∂f do not existCfff is not continuous and ∂f∂x\frac{\partial f}{\partial x}∂x∂f and ∂f∂y\frac{\partial f}{\partial y}∂y∂f existDfff is not continuous and ∂f∂x\frac{\partial f}{\partial x}∂x∂f and ∂f∂y\frac{\partial f}{\partial y}∂y∂f do not existPick an option to check your answer.Show answerShow solution Report a problem with this question← Q4All questionsQ6 →Keyboard: A–D answer · S solution · ←/→ previous/next