4.7: L'Hôpital's Rule
- Page ID
- 144289
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- Compute \(\displaystyle \lim_{x \to 0} \dfrac{\sin x}{x}\).
- Compute \(\displaystyle \lim_{x \to 0} \dfrac{1 - \cos x}{x}\).
- Compute \(\displaystyle \lim_{x \to 2} \dfrac{x - 2}{x^2 - 4}\).
- Compute \(\displaystyle \lim_{x \to 3} \dfrac{x - 1}{x^2 + 2x - 5}\).
- Computer \(\displaystyle \lim_{x \to 0} \dfrac{e^x - 1}{x}\).
- Compute \(\displaystyle \lim_{x \to \pi} \dfrac{x - \pi}{\sin x}\).
- Compute \(\displaystyle \lim_{x \to 1} \dfrac{x - 1}{\sin 1}\).
- Compute \(\displaystyle \lim_{x \to \infty} \dfrac{3x^2 - 2x + 5}{2x - 6x^2}\).
- Compute \(\displaystyle \lim_{x \to \infty} \dfrac{\sin x}{x}\).
- Compute \(\displaystyle \lim_{x \to 0} \dfrac{1 + \dfrac{1}{x}}{1 - \dfrac{1}{x}}\).
- Compute \(\displaystyle \lim_{x \to 0^+} x\ln x\).
- Compute \(\displaystyle \lim_{x \to \infty} x^2 \ln x\).
- Compute \(\displaystyle \lim_{x \to -\infty} (\sqrt{x^2 + 1} - \sqrt{x^2})\).
- Compute \(\displaystyle \lim_{x \to \infty} (\sqrt{x^2 + 1} + \sqrt{x^2})\).
- Compute \(\displaystyle \lim_{x \to 0^+} x^{1/x}\).
- Compute \(\displaystyle \lim_{x \to \infty} \left(1 + \dfrac{1}{x}\right)^x\).
- Compute \(\displaystyle \lim_{x \to 0} \left(1 + \dfrac{1}{x} \right)^x\).