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Question
\[\lim_{x \to - 1} \frac{x^3 + 1}{x + 1}\]
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Solution
\[\lim_{x \to - 1} \left[ \frac{x^3 + 1}{x + 1} \right]\]
\[\text{ It is of the form } \frac{0}{0} . \]
\[ \lim_{x \to - 1} \left[ \frac{x^3 + 1^3}{x + 1} \right]\]
\[ = \lim_{x \to - 1} \left[ \frac{\left( x + 1 \right)\left( x^2 - x + 1 \right)}{\left( x + 1 \right)} \right]\]
\[ = \left( - 1 \right)^2 - \left( - 1 \right) + 1\]
\[ = 1 + 1 + 1\]
\[ = 3\]
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