I need to check for which values of "k" the following function is continuous at (0,0):
\(\displaystyle \LARGE{f(x,y)=\left\{ \begin{array}{1 1} \frac{\sin(x^2)\cdot|y|^{k+1}}{x^4+y^2} & (x,y)\ne(0,0) \\ 0 & (x,y)=(0,0) \\ \end{array} \right.}\)
In other words, I need to check when:
\(\displaystyle \LARGE{\lim_{(x,y)\to(0,0)}{\frac{\sin(x^2)\cdot|y|^{k+1}}{x^4+y^2}}=0}\)
Can someone please give me a direction?
Should I use polar coordinates?
\(\displaystyle \LARGE{f(x,y)=\left\{ \begin{array}{1 1} \frac{\sin(x^2)\cdot|y|^{k+1}}{x^4+y^2} & (x,y)\ne(0,0) \\ 0 & (x,y)=(0,0) \\ \end{array} \right.}\)
In other words, I need to check when:
\(\displaystyle \LARGE{\lim_{(x,y)\to(0,0)}{\frac{\sin(x^2)\cdot|y|^{k+1}}{x^4+y^2}}=0}\)
Can someone please give me a direction?
Should I use polar coordinates?