Original
Justification: Notice that {{MATH_67}}, where
{{MATH_68}}
The function {{MATH_69}} is {{CMD_70}}{{CMD_71}}not continuous{{CMD_72}}{{CMD_73}}continuous{{CMD_74}}{{CMD_75}} on {{MATH_76}}.{{CMD_77}}
The function {{MATH_78}} is a {{CMD_79}}{{CMD_80}}product{{CMD_81}}{{CMD_82}}sum{{CMD_83}}{{CMD_84}} of two continuous functions, {{MATH_85}} and {{MATH_86}}.
Therefore, {{MATH_87}} is {{CMD_88}}{{CMD_89}}not continuous{{CMD_90}}{{CMD_91}}continuous{{CMD_92}}{{CMD_93}} on its domain {{MATH_94}}.{{CMD_95}}
So, we can apply
{{CMD_96}}{{CMD_97}}Composition{{CMD_98}}{{CMD_99}}Product{{CMD_100}}{{CMD_101}} limit law
{{MATH_102}}
Since {{MATH_103}} is {{CMD_104}}{{CMD_105}}not continuous{{CMD_106}}{{CMD_107}}continuous{{CMD_108}}{{CMD_109}} at {{MATH_110}}, we have
{{MATH_111}}
and, therefore
{{MATH_112}}
{{CMD_113}}{{CMD_114}}
{{CMD_115}}
{{CMD_116}}
{{CMD_117}}