Question: Calculate the following limits, if they exist:

1. \(\underset{\left( x,y \right)\to \left( 0,0 \right)}{\mathop{\lim }}\,\left( {{x}^{2}}+{{y}^{2}}+4 \right)\)
2. \(\underset{\left( x,y \right)\to \left( 0,0 \right)}{\mathop{\lim }}\,\frac{xy}{{{x}^{2}}+{{y}^{2}}+4}\)
3. \(\underset{\left( x,y \right)\to \left( 0,0 \right)}{\mathop{\lim }}\,\frac{{{\left( x-y \right)}^{2}}}{{{x}^{2}}+{{y}^{2}}}\)
4. \(\underset{\left( x,y \right)\to \left( 0,0 \right)}{\mathop{\lim }}\,\frac{2\cos x-2-{{x}^{2}}}{{{x}^{4}}+{{y}^{4}}}\)

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