Applications of derivatives

1003163901

Level:

Use L'Hospital's rule to find the following limit.

lim_{x \to 2} \frac{2 x^{3} - 3 x^{2} - 4}{x^{2} + x - 6}

\frac{12}{5}

\frac{18}{5}

\frac{12}{3}

0

\infty

Level:

Use L'Hospital's rule to find the following limit.

lim_{x \to 0} \frac{e^{x} - 1}{\sin 2 x}

\frac{1}{2}

- \frac{1}{2}

1

0

- 1

Level:

Use L'Hospital's rule to find the following limit.

lim_{x \to 0} \frac{\sin 2 x}{tg 3 x}

\frac{2}{3}

1

2

0

6

Level:

Use L'Hospital's rule to find the following limit.

lim_{x \to \frac{π}{3}} \frac{1 - 2 \cos x}{π - 3 x}

- \frac{\sqrt{3}}{3}

- \frac{\sqrt{3}}{6}

\frac{\sqrt{3}}{3}

\frac{\sqrt{3}}{6}

- \frac{1}{3}

Level:

Use L'Hospital's rule to find the following limit.

lim_{x \to 1} \frac{\sqrt{x + 3} - 2}{\ln x}

\frac{1}{4}

\frac{1}{2}

0

1

\frac{\sqrt{2}}{2}

Level:

Evaluate the following limit. (Apply L'Hospital's rule repeatedly.)

lim_{x \to \infty} \frac{x^{2} - 1}{x^{3} - 2 x^{2} + x}

0

\infty

\frac{2}{3}

1

Level:

Evaluate the following limit. (Apply L'Hospital's rule repeatedly.)

lim_{x \to \infty} \frac{e^{x} - 2}{x^{2}}

\infty

0

1

\frac{1}{2}

Level:

Evaluate the following limit. (Apply L'Hospital's rule repeatedly.)

lim_{x \to 1} \frac{\cos (π x) + 1}{(x - 1)^{2}}

\frac{π^{2}}{2}

- \frac{π^{2}}{2}

\frac{π}{2}

- \frac{π}{2}

Level:

Evaluate the following limit. (Apply L'Hospital's rule repeatedly.)

lim_{x \to 0} \frac{x - \sin x}{x^{3}}

\frac{1}{6}

- \frac{1}{6}

\frac{1}{3}

- \frac{1}{3}

0

Level:

Use L'Hospital's rule to find the following limit.

lim_{x \to 2} \frac{x^{3} - 4 x^{2} + 8}{2 x^{2} - 3 x - 2}

- \frac{4}{5}

\frac{4}{5}

- 4

0

\infty