# Multivariate Calculus: multivariate calculus – #28070

Question: Calculate the following limits, if they exist:

(a) $$\underset{\left( x,y \right)\to \left( 0,0 \right)}{\mathop{\lim }}\,\left( {{x}^{2}}+{{y}^{2}}+4 \right)$$

(b) $$\underset{\left( x,y \right)\to \left( 0,0 \right)}{\mathop{\lim }}\,\frac{xy}{{{x}^{2}}+{{y}^{2}}+4}$$

(c) $$\underset{\left( x,y \right)\to \left( 0,0 \right)}{\mathop{\lim }}\,\frac{{{\left( x-y \right)}^{2}}}{{{x}^{2}}+{{y}^{2}}}$$

(d) $$\underset{\left( x,y \right)\to \left( 0,0 \right)}{\mathop{\lim }}\,\frac{2\cos x-2-{{x}^{2}}}{{{x}^{4}}+{{y}^{4}}}$$