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To find the limit of
as
approaches
, simply substitute
into the polynomial. This means we calculate
, leading to
.
Next up, for the limit
, plug in
. Here, both the numerator and denominator become
when evaluated directly, which suggests the use of L’Hôpital’s Rule. Differentiating the numerator and denominator gives us
after calculating the derivatives and simplifying.
For the final limit,
, notice that
can be factored to
. This allows the
terms to cancel, so we rewrite the limit as
, which simplifies to
when substituting
into the resulting expression.