Section 13.1 : Limits
1. Evaluate the following limit.
\[\mathop {\lim }\limits_{\left( {x,y,z} \right) \to \left( { - 1,0,4} \right)} \frac{{{x^3} - z{{\bf{e}}^{2y}}}}{{6x + 2y - 3z}}\] Show SolutionIn this case there really isn’t all that much to do. We can see that the denominator exists and will not be zero at the point in question and the numerator also exists at the point in question. Therefore, all we need to do is plug in the point to evaluate the limit.
\[\mathop {\lim }\limits_{\left( {x,y,z} \right) \to \left( { - 1,0,4} \right)} \frac{{{x^3} - z{{\bf{e}}^{2y}}}}{{6x + 2y - 3z}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{5}{{18}}}}\]