AP Calculus ABmediummcq1 pt
If lim(x→0) (sin(3x)/x) = L, what is the value of L?
A.0
B.1
C.3
D.∞
Explanation
Core Concept
This is a standard limit that can be evaluated using L'Hôpital's Rule since it's in the indeterminate form 0/0. Differentiating numerator and denominator: lim(x→0) (3cos(3x)/1) = 3cos(0) = 3. Alternatively, recognizing this as a standard limit form: lim(x→0) (sin(ax)/x) = a.
Correct Answer
C3
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 $\displaystyle\lim_{x\to 0}\dfrac{1-\cos x}{x^2}$?
- hardWhat is $\displaystyle\lim_{x\to 0}\dfrac{e^x-1-x}{x^2}$?
Practice more AP Calculus AB questions with full explanations
Practice Unit 4: Contextual Applications of Differentiation Questions →