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Question
\[\lim_{x \to - 5} \frac{2 x^2 + 9x - 5}{x + 5}\]
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Solution
\[\lim_{x \to - 5} \left[ \frac{2 x^2 + 9x - 5}{x + 5} \right]\]
\[\text{ It is of the form }\frac{0}{0} . \]
\[ \lim_{x \to - 5} \left[ \frac{2 x^2 + 10x - x - 5}{x + 5} \right]\]
\[ = \lim_{x \to - 5} \left[ \frac{2x\left( x + 5 \right) - 1\left( x + 5 \right)}{x + 5} \right]\]
\[ = \lim_{x \to - 5} \left[ \frac{\left( 2x - 1 \right)\left( x + 5 \right)}{x + 5} \right]\]
\[ = \lim_{x \to - 5} \left( 2x - 1 \right)\]
\[ = 2\left( - 5 \right) - 1\]
\[ = - 11\]
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