5.13 Limits and l'Hôpital's rule Quiz

1. Find $\lim_{x\to0}\dfrac{\tan 3x}{x}$.

• A. $0$
• B. $1$
• C. $3$
• D. $\dfrac{1}{3}$

2. Find $\lim_{x\to0}\dfrac{e^{x} - 1 - x}{x^{2}}$.

• A. $1$
• B. $\dfrac{1}{2}$
• C. $0$
• D. $2$

3. Find $\lim_{x\to\infty}\dfrac{3x + \ln x}{x}$.

• A. $\infty$
• B. $1$
• C. $4$
• D. $3$

4. Why can l'Hôpital's rule NOT be used on $\lim_{x\to0}\dfrac{\cos x}{x + 1}$?

• A. The limit is infinite
• B. It is not an indeterminate form; substitution gives $1$
• C. Cosine cannot be differentiated
• D. The denominator is linear

5. Using $\sin x = x - \dfrac{x^{3}}{6} + \cdots$, find $\lim_{x\to0}\dfrac{\sin x - x}{x^{3}}$.

• A. $-\dfrac{1}{6}$
• B. $\dfrac{1}{6}$
• C. $0$
• D. $-1$