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}}