Let f:RtimesRtoR be a function defined by f(x, y)=begincases xy(x+y)/x^2+y^2, & if (x, y)neq (0, 0), 0, & if (x, y)=(0, 0). endcases Then, which of the following statements is/are TRUE?

Q36Section B (Section B)36 of 60

Differentiability of rational bivariate function

Let $f:\mathbb{R}\times\mathbb{R}\to\mathbb{R}$ be a function defined by $f(x, y)=\begin{cases} \frac{xy(x+y)}{x^2+y^2}, & \text{if }(x, y)\neq (0, 0), \ 0, & \text{if }(x, y)=(0, 0). \end{cases}$ Then, which of the following statements is/are TRUE?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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