Let a,b be distinct positive real numbers. Consider the function f:R^2toR given by f(x,y)=begincases(ax+by)^2/ax^2+by^2 & if (x,y)neq(0,0), 0 & if (x,y)=(0,0).endcases Which of the following statements are necessarily true?

Q68Section C (Part C)68 of 120

Several variables — a homogeneous quotient at the origin

Let $a,b$ be distinct positive real numbers. Consider the function $f:\mathbb{R}^2\to\mathbb{R}$ given by

$f(x,y)=\begin{cases}\dfrac{(ax+by)^2}{ax^2+by^2} & \text{if }(x,y)\neq(0,0),\\ 0 & \text{if }(x,y)=(0,0).\end{cases}$

Which of the following statements are necessarily 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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