Calculus Problems

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  1. \(\lim_{ \theta \rightarrow 0} \frac{\cos(\theta) - 1}{\theta}\)

  2. \(\lim_{\theta \rightarrow 0} \frac{\sec{(2\theta)} \tan{(3 \theta)}}{5 \theta} \)

  3. \(\lim_{x \rightarrow 0} \frac{\tan{x}}{x} \)

  4. \(\lim_{x \rightarrow 0} \frac{\sin{(3x)}}{x} \)

  5. \(\lim_{x \rightarrow \infty}\frac{2x - 1}{x + 1} \)

  6. \(\lim_{x \rightarrow \infty}\frac{3x^2 - 5x + 1}{x^3 - 1} \)

  7. \(\lim_{x \rightarrow -\infty} \frac{x}{\sqrt{x^2 + 1}}\)

  8. \(\lim_{x \rightarrow \infty} \frac{2x + 1}{\sqrt{x^2 - x}} \)

  9. \(\lim_{x\rightarrow \infty}\sin\frac{1}{x} \)

  10. \(\lim_{x \rightarrow \infty}(\frac{5}{x} - \arctan{x}) \)

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