IMathAS-libretexts

In the following problems you will find the limit of a function numerically (i.e. from a table). Find the value of the limit from the table of functional values in the table. If the limit does not exist, state this.

A)

\displaystyle {y}={\frac{{{\cos{{x}}}-{1}}}{{{x}}}}

$\displaystyle \lim_{{{x}\to{0}}}{\frac{{{\cos{{x}}}-{1}}}{{{x}}}}=$
$\displaystyle \lim_{{{x}\to{0}}}{\frac{{{\cos{{x}}}-{1}}}{{{x}}}}$ DNE
$\displaystyle \lim_{{{x}\to{0}}}{\frac{{{\cos{{x}}}-{1}}}{{{x}}}}$ UND

\displaystyle {y}={\frac{{{e}^{{x}}-{1}}}{{{x}}}}

$\displaystyle \lim_{{{x}\to{0}}}{\frac{{{e}^{{x}}-{1}}}{{{x}}}}=$
$\displaystyle \lim_{{{x}\to{0}}}{\frac{{{e}^{{x}}-{1}}}{{{x}}}}$ DNE
$\displaystyle \lim_{{{x}\to{0}}}{\frac{{{e}^{{x}}-{1}}}{{{x}}}}$ UND

\displaystyle {y}={\frac{{{\left|{x}-{1}\right|}}}{{{x}-{1}}}}

$\displaystyle \lim_{{{x}\to{1}}}{\frac{{{\left|{x}-{1}\right|}}}{{{x}-{1}}}}=$
$\displaystyle \lim_{{{x}\to{1}}}{\frac{{{\left|{x}-{1}\right|}}}{{{x}-{1}}}}$ DNE
$\displaystyle \lim_{{{x}\to{1}}}{\frac{{{\left|{x}-{1}\right|}}}{{{x}-{1}}}}$ UND

\displaystyle {y}={\frac{{{\sin{{x}}}}}{{{x}}}}

$\displaystyle \lim_{{{x}\to{0}}}{\frac{{{\sin{{x}}}}}{{{x}}}}=$
$\displaystyle \lim_{{{x}\to{0}}}{\frac{{{\sin{{x}}}}}{{{x}}}}$ DNE
$\displaystyle \lim_{{{x}\to{0}}}{\frac{{{\sin{{x}}}}}{{{x}}}}$ UND

\displaystyle {y}={\frac{{{x}+{1}}}{{{x}^{{2}}-{1}}}}

$\displaystyle \lim_{{{x}\to{1}}}{\frac{{{x}+{1}}}{{{x}^{{2}}-{1}}}}=$
$\displaystyle \lim_{{{x}\to{1}}}{\frac{{{x}+{1}}}{{{x}^{{2}}-{1}}}}$ DNE
$\displaystyle \lim_{{{x}\to{1}}}{\frac{{{x}+{1}}}{{{x}^{{2}}-{1}}}}$ UND

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