Apentix/AP Calculus AB/Unit 4: Contextual Applications of Differentiation/Question

AP Calculus ABhardmcq1 pt

What is $\displaystyle\lim_{x\to 0}\dfrac{e^x-1-x}{x^2}$ ?

A.

0

B.

1

C.

2

D.

\dfrac{1}{2}

Explanation

Core Concept

The form is $\dfrac{0}{0}$ . Applying L'Hôpital's rule twice gives $\dfrac{e^x-1}{2x}\to\dfrac{e^x}{2}\to\dfrac{1}{2}$ .

Correct Answer

D $\dfrac{1}{2}$

More Unit 4: Contextual Applications of Differentiation practice questions

hardAt noon, ship A is 100 km west of ship B. Ship A sails east at 20 km/h and ship B sails north at 15 km/h. How fast is the distance between t…
hardWater drains from an inverted conical tank 10 m tall with a top radius of 5 m at a rate of 2 m$^3$/min. How fast is the depth of the water d…
hardWhat is $\displaystyle\lim_{x\to\infty}\dfrac{x^3}{e^x}$?
hardWhat is $\displaystyle\lim_{x\to 0}\dfrac{1-\cos x}{x^2}$?
hardA rocket rises vertically at 12 ft/s from a launch pad, passing a camera 12 ft away. When the rocket is 5 ft above the pad, how fast is the …

Try a random question →

Practice more AP Calculus AB questions with full explanations

Practice Unit 4: Contextual Applications of Differentiation Questions →