## Calculus (3rd Edition)

$$\lim _{x \rightarrow-\frac{1}{2}} \frac{2 x+1}{2 x^{2}+3 x+1}=2$$
Given $$\lim _{x \rightarrow-\frac{1}{2}} \frac{2 x+1}{2 x^{2}+3 x+1}$$ let $$f(x) = \frac{2 x+1}{2 x^{2}+3 x+1}$$ Since, we have $$f(-\frac{1}{2})= \frac{-1+1}{\frac{1}{2}-\frac{3}{2}+1}=\frac{0}{0}$$ So, transform algebraically and cancel \begin{aligned} L&=\lim _{x \rightarrow-\frac{1}{2}} \frac{2 x+1}{2 x^{2}+3 x+1}\\ &=\lim _{x \rightarrow -\frac{1}{2}} \frac{(2x+1)}{(2x+1)(x+1)}\\ &=\lim _{x \rightarrow -\frac{1}{2}} \frac{1}{(x+1)}\\ &= \frac{1}{(-\frac{1}{2}+1)}\\ &= \frac{1}{(\frac{1}{2})}\\ &=2 \end{aligned}
The text passage contains a calculus problem involving the evaluation of a limit, and it provides a detailed solution to the problem.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
## Calculus (3rd Edition)

$$\lim _{x \rightarrow-\frac{1}{2}} \frac{2 x+1}{2 x^{2}+3 x+1}=2$$
Given $$\lim _{x \rightarrow-\frac{1}{2}} \frac{2 x+1}{2 x^{2}+3 x+1}$$ let $$f(x) = \frac{2 x+1}{2 x^{2}+3 x+1}$$ Since, we have $$f(-\frac{1}{2})= \frac{-1+1}{\frac{1}{2}-\frac{3}{2}+1}=\frac{0}{0}$$ So, transform algebraically and cancel \begin{aligned} L&=\lim _{x \rightarrow-\frac{1}{2}} \frac{2 x+1}{2 x^{2}+3 x+1}\\ &=\lim _{x \rightarrow -\frac{1}{2}} \frac{(2x+1)}{(2x+1)(x+1)}\\ &=\lim _{x \rightarrow -\frac{1}{2}} \frac{1}{(x+1)}\\ &= \frac{1}{(-\frac{1}{2}+1)}\\ &= \frac{1}{(\frac{1}{2})}\\ &=2 \end{aligned}
user
The text passage contains a calculus problem involving the evaluation of a limit, and it provides a detailed solution to the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER