Original
Evaluate the limit and justify your answer.{{CMD_1}}
{{CMD_2}}
{{CMD_3}}
{{MATH_4}}
Justification:{{CMD_5}}
Notice that {{MATH_6}}, where
{{MATH_7}}
and both functions, {{MATH_8}} and {{MATH_9}}, are {{CMD_10}}{{CMD_11}}not continuous{{CMD_12}}{{CMD_13}}continuous{{CMD_14}}{{CMD_15}} on {{MATH_16}}.{{CMD_17}}
So, we can apply
{{CMD_18}}{{CMD_19}}Composition{{CMD_20}}{{CMD_21}}Product{{CMD_22}}{{CMD_23}} limit law
{{MATH_24}}
Since {{MATH_25}} is {{CMD_26}}{{CMD_27}}not continuous{{CMD_28}}{{CMD_29}}continuous{{CMD_30}}{{CMD_31}} at {{MATH_32}}, we have
{{MATH_33}}
and, therefore
{{MATH_34}}
{{CMD_35}}{{CMD_36}}