Let {{MATH_1}} Determine if the following limits exist. If they exist, compute them {{CMD_2}}analytically{{CMD_3}} using the {{CMD_4}}limit laws{{CMD_5}} and {{CMD_6}}techniques for computing limits{{CMD_7}}. If a limit {{CMD_8}}does not exist{{CMD_9}}, write `DNE' and explain why. Do not use a table of values, a graph, or L'H{{CMD_10}}opital's rule to justify your answer. {{CMD_11}} {{MATH_12}} {{CMD_13}} {{CMD_14}} {{MATH_15}} {{CMD_16}} {{CMD_17}} {{MATH_18}} {{CMD_19}} Let's give an explanation as to why this is true. When {{MATH_20}} is greater than {{MATH_21}}, {{MATH_22}} {{CMD_23}}As {{MATH_24}} approaches {{MATH_25}} from the right, {{MATH_26}} is {{CMD_27}}{{CMD_28}}positive{{CMD_29}}{{CMD_30}}negative{{CMD_31}}{{CMD_32}}zero{{CMD_33}}{{CMD_34}} and approaching zero while at the same time, {{MATH_35}} approaches {{MATH_36}}. {{CMD_37}} Therefore, as {{MATH_38}} approaches {{MATH_39}} from the right, {{MATH_40}} is positive and grows {{CMD_41}}{{CMD_42}}arbitrarily large{{CMD_43}}{{CMD_44}}arbitrarily small{{CMD_45}}{{CMD_46}}. {{CMD_47}} Hence, {{MATH_48}} {{CMD_49}} {{CMD_50}} {{CMD_51}} {{CMD_52}} {{CMD_53}} {{MATH_54}} {{CMD_55}} {{CMD_56}} {{MATH_57}} {{CMD_58}} {{CMD_59}} List the vertical asymptotes of {{MATH_60}} from least to greatest: {{MATH_61}}. {{CMD_62}} {{CMD_63}} List all the horizontal asymptotes of {{MATH_64}} from least to greatest: {{MATH_65}}. {{CMD_66}} {{CMD_67}} {{CMD_68}}