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

   Which 1969 NASA mission used calculus to reach the moon?

   Answer: Apollo 11

   Why: Eagle's guidance computer had just 2,048 words of erasable memory, and its program was threaded by hand through magnetic cores.

2. 2 Medium

   What two ideas does the Fundamental Theorem of Calculus link?

   Answer: Differentiation and integration

   Why: Scottish mathematician James Gregory published the first proof of it in 1668, framed as geometry and only for a special class of curves.

3. 3 Hard

   What constant is the limit of $(1 + 1/n)^n$ as $n$ approaches infinity?

   Answer: $e$

   Why: Jacob Bernoulli hit this limit in 1683 asking what nonstop compound interest pays, and Euler was already writing e for it in 1731.

4. 4 Easy

   Which mathematician developed calculus independently of Isaac Newton in the 1670s?

   Answer: Gottfried Wilhelm Leibniz

   Why: Leibniz published the first calculus paper in 1684, yet a 1712 Royal Society report steered by Newton as its president ruled against him.

5. 5 Medium

   Which paradox did calculus finally solve using infinite series?

   Answer: Zeno's Paradox

   Why: Zeno's own book is lost: Aristotle preserved his four arguments against motion, and philosophers still debate whether maths settles them.

6. 6 Hard

   What is the derivative of $\tan(x)$ with respect to $x$?

   Answer: $\sec^2(x)$

   Why: The same derivative can be written as tan^2(x) plus one, so it never vanishes and the tangent curve keeps rising between its vertical asymptotes.