For item {{CMD_57}}, in order to compute the limit we will have to compute two one-sided limits (since the expression for {{MATH_58}} if {{MATH_59}} is different from the expression for {{MATH_60}} if {{MATH_61}}). {{ENV_62}} and {{ENV_63}} In order for {{MATH_64}} to exist, {{MATH_65}} So, if {{MATH_66}}, the limit {{MATH_67}} which means item {{CMD_68}} is satisfied. For item {{CMD_69}} we need to check that the value we found for {{MATH_70}} is the same as the value we found for {{MATH_71}}. These values agree, so item {{CMD_72}} is satisfied. This proves that {{MATH_73}} is continuous at {{MATH_74}}. {{CMD_75}} {{CMD_76}} {{CMD_77}} In the previous example, notice that finding the value of {{MATH_78}} is not where the work ended. In order to justify the answer, we have to verify that all three conditions of the checklist are satisfied for the value we found. {{CMD_79}}