text: ## 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}
explanation: The document contains a detailed solution to a calculus problem involving the evaluation of a limit. The problem is presented, and the steps to solve it are shown, including the algebraic transformation and simplification. The final answer is provided.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: ## 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}
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a detailed solution to a calculus problem involving the evaluation of a limit. The problem is presented, and the steps to solve it are shown, including the algebraic transformation and simplification. The final answer is provided.
  
  Label: question-and-answer