Calculus quiz

More questions about Calculus

These visible examples show the question style. LearnClash turns the full topic into ranked duels and spaced repetition.

1. 1 Easy

   What is the limit of $\frac{\sin(x)}{x}$ as $x$ approaches $0$?

   Answer: $1$

   Why: Switch the angle to degrees and this same limit drops to π/180, about 0.0175, which is why calculus measures angles in radians.

2. 2 Medium

   The 'disk method' is used to calculate what property of a solid?

   Answer: volume

   Why: Kepler did it by hand in 1615, treating each wine barrel as a stack of thin cylinders after a merchant's measuring rod annoyed him.

3. 3 Hard

   In physics, what is the third derivative of position called?

   Answer: jerk

   Why: Keep differentiating and the names get silly: the fourth derivative is snap, and the fifth and sixth are jokingly crackle and pop.

4. 4 Easy

   What does the area under a velocity-time graph represent in physics?

   Answer: displacement

   Why: Nicole Oresme plotted speed against time around 1350 and read the distance travelled straight off the area, centuries before calculus existed.

5. 5 Medium

   Integration by parts is the reverse operation of which differentiation rule?

   Answer: Product Rule

   Why: Brook Taylor published the method in 1715; the LIATE mnemonic still tells students which factor to choose as u.

6. 6 Hard

   The brachistochrone curve, solved using calculus, takes what geometric shape?

   Answer: cycloid

   Why: The same curve is the tautochrone: Huygens proved in 1659 that a bead released anywhere on it reaches the bottom in exactly the same time.