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Let \[ f(x, y)=\left\{\begin{array}{ll} \frac{(x+y)^{2}}{x^{2}+y^{2}} & \text { if }(x, y) \neq(0, ...
Let \[ f(x, y)=\left\{\begin{array}{ll} \frac{(x+y)^{2}}{x^{2}+y^{2}} & \text { if }(x, y) \neq(0,0) \\ 1 & \text { if }(x, y)=(0,0) \end{array}\right. \] (a) Evaluate the limit of \( f(x, y) \) when \( (x, y) \) approaches \( (0,0) \) along the line \( x=0, y=0 \) and \( y=k x \) for \( k \in \mathbb{R} \backslash\{0\} \). (b) Determine where \( f(x, y) \) is continuous. Justify your answer. (c) Determine where \( f(x, y) \) is \( C^{1} \). Justify your answer.