Original
Compute the following limits using Limit Laws:
{{CMD_44}}
{{CMD_45}}{{CMD_46}} {{MATH_47}}
{{CMD_48}}{{CMD_49}} {{MATH_50}}
{{CMD_51}}{{CMD_52}} {{MATH_53}}
{{CMD_54}}{{CMD_55}} {{MATH_56}}
{{CMD_57}}
{{CMD_58}}
For {{MATH_59}}, write:
{{ENV_60}}
For {{MATH_61}}, write:
{{ENV_62}}
For {{MATH_63}}, using the Product Law, we can write:
{{MATH_64}}
{{ENV_65}}
For {{MATH_66}}, write:
{{MATH_67}}
The function {{MATH_68}} is a combination of the functions
{{MATH_69}} and {{MATH_70}}, but it is neither a sum/difference, nor a
product, nor a quotient of these two functions, so we cannot apply
any of the Limit Laws. This function is a composition of the two
functions, {{MATH_71}} and {{MATH_72}}.
{{CMD_73}}
{{CMD_74}}
{{CMD_75}}
{{CMD_76}}
{{CMD_77}} Compute the following limit using limit laws:
{{MATH_78}}
{{CMD_79}}
Well, get out your pencil and write with me:
{{MATH_80}}
by the Sum/Difference Law. So now
{{MATH_81}}
by the Product Law. Finally by continuity of {{MATH_82}} and {{MATH_83}},
{{MATH_84}}
{{CMD_85}}
We can check our answer by looking at the graph of {{MATH_86}}:
{{MATH_87}}
{{CMD_88}}
{{CMD_89}}