Question Number 195195 by Mr.D.N. last updated on 26/Jul/23
$$\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{limit}: \\ $$$$\:\underset{\mathrm{x}\rightarrow\mathrm{a}\:} {\overset{\mathrm{lim}} {\:}}\:\:\:\frac{\boldsymbol{\mathrm{x}}^{\frac{\mathrm{1}}{\mathrm{3}}} }{\boldsymbol{\mathrm{x}}^{\frac{\mathrm{1}}{\mathrm{2}}} }\:−\:\frac{\boldsymbol{\mathrm{a}}^{\frac{\mathrm{1}}{\mathrm{3}}} }{\boldsymbol{\mathrm{a}}^{\frac{\mathrm{1}}{\mathrm{2}}} } \\ $$
Commented by Frix last updated on 26/Jul/23
$$\mathrm{Obviously}\:\mathrm{0} \\ $$
Answered by som(math1967) last updated on 27/Jul/23
$$\:\underset{\boldsymbol{{x}}\rightarrow\boldsymbol{{a}}} {{lim}}\:\frac{\mathrm{1}}{\boldsymbol{{x}}^{\frac{\mathrm{1}}{\mathrm{6}}} }\:−\frac{\mathrm{1}}{\boldsymbol{{a}}^{\frac{\mathrm{1}}{\mathrm{6}}} } \\ $$$$\:\:\frac{\mathrm{1}}{\boldsymbol{{a}}^{\frac{\mathrm{1}}{\mathrm{6}}} }\:−\frac{\mathrm{1}}{\boldsymbol{{a}}^{\frac{\mathrm{1}}{\mathrm{6}}} }=\mathrm{0} \\ $$