The expression is
.
Graph the function
.
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Observe the graph:
\As
tends to
from left hand side,
approaches to
.
As
tends to
from right hand side,
approaches to
.
Since left hand side limit is equal to right hand side limit, then the limit exists.
\
.
Draw a table to find the value of the limit.
\![]() | \
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Observe the table.
\The value of
at
is
.
The value of
at
is
.
The value of
at
is
.
The expression is
.
Rationalize the numerator.
\
Apply product rule of limits.
\
Apply special trigonometric limits
.


.
.
.