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Section 13.1 : Limits

Evaluate each of the following limits.

1. \(\displaystyle \mathop {\lim }\limits_{\left( {x,y,z} \right) \to \left( { - 1,0,4} \right)} \frac{{{x^3} - z{{\bf{e}}^{2y}}}}{{6x + 2y - 3z}}\) Solution
2. \(\displaystyle \mathop {\lim }\limits_{\left( {x,y} \right) \to \left( {2,1} \right)} \frac{{{x^2} - 2xy}}{{{x^2} - 4{y^2}}}\) Solution
3. \(\displaystyle \mathop {\lim }\limits_{\left( {x,y} \right) \to \left( {0,0} \right)} \frac{{x - 4y}}{{6y + 7x}}\) Solution
4. \(\displaystyle \mathop {\lim }\limits_{\left( {x,y} \right) \to \left( {0,0} \right)} \frac{{{x^2} - {y^6}}}{{x{y^3}}}\) Solution