Original
Compute:
{{MATH_113}}
{{CMD_114}}
The function {{MATH_115}} is of the form {{MATH_116}} for a positive real number
{{MATH_117}}. Therefore, {{MATH_118}} is continuous for all positive real values of
{{MATH_119}}. In particular, {{MATH_120}} is continuous at {{MATH_121}}. Since {{MATH_122}}
is continuous at {{MATH_123}}, we know that {{MATH_124}}.
That is, {{MATH_125}}.
{{CMD_126}}
{{CMD_127}}
{{CMD_128}}
Compute:
{{MATH_129}}
{{CMD_130}}
The function {{MATH_131}} is a constant.
Therefore, {{MATH_132}} is continuous for all real values of
{{MATH_133}}. In particular, {{MATH_134}} is continuous at {{MATH_135}}. Since {{MATH_136}}
is continuous at {{MATH_137}}, we know that {{MATH_138}}.
That is, {{MATH_139}}.
{{CMD_140}}
{{CMD_141}}
{{CMD_142}}
Compute:
{{MATH_143}}
{{CMD_144}}
The function {{MATH_145}} is contionuous
for all real values of
{{MATH_146}}. In particular, {{MATH_147}} is continuous at {{MATH_148}}. Since {{MATH_149}}
is continuous at {{MATH_150}}, we know that {{MATH_151}}.
That is, {{MATH_152}}.
{{CMD_153}}
{{CMD_154}}