Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.
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.
\[\mathop {\lim }\limits_{\left( {x,y,z} \right) \to \left( { - 1,0,4} \right)} \frac{{{x^3} - z{{\bf{e}}^{2y}}}}{{6x + 2y - 3z}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{5}{{18}}}}\]