Consider {{MATH_133}}. Fill in the tables below {{CMD_134}}rounding to three decimal places{{CMD_135}}: {{MATH_136}} We may rush and say that, based on the table above, {{MATH_137}} But, recall the definition of the limit: {{MATH_138}} is the limit if the value of {{MATH_139}} is as close as one wishes to {{MATH_140}} for {{CMD_141}}all{{CMD_142}} {{MATH_143}} sufficiently close, but not equal to, {{MATH_144}}. From this table we can see that {{MATH_145}} is as close as one wishes to {{MATH_146}} for {{CMD_147}}some{{CMD_148}} values {{MATH_149}} that are sufficiently close to {{MATH_150}}. But this does does not satisfy the definition of the limit, at least, not yet. But, wait! Fill in another table, {{CMD_151}}rounding to three decimal places{{CMD_152}}. {{MATH_153}} What do these two tables tell us about {{MATH_154}} {{CMD_155}} {{CMD_156}}{{MATH_157}}{{CMD_158}} {{CMD_159}}{{MATH_160}}{{CMD_161}} {{CMD_162}}{{MATH_163}}{{CMD_164}} {{CMD_165}}{{MATH_166}}{{CMD_167}} {{CMD_168}}The limit does not exist.{{CMD_169}} {{CMD_170}} {{CMD_171}} The limit does not exist.