Mathematics & Logic

Survive the Calculus Gauntlet: Fierce Foes Await

Battle through five savage calculus problems on series, derivatives, theorems, and integrals to claim mathematical supremacy.

#improper integrals#hard calculus#math logic puzzles#advanced integration#multivariable calc#series radius#greens theorem#mixed partials#taylor maclaurin#power series

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Total Questions

Difficulty Level

hard

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Quiz Questions

Answer all questions below and test your knowledge.

1
What is the radius of convergence of the power series sum from n=1 to infinity of (n! / n^n) x^n?
Question 1
2
In the Maclaurin series expansion of ln(1 + x), the coefficient of the x^4 term is:
Question 2
3
For the function f(x, y) = x^2 y + sin(x y), compute the mixed partial derivative f_{xy}(0, 0).
Question 3
4
By Green's theorem, the counterclockwise line integral around the unit circle of -y dx + x dy equals:
Question 4
5
Evaluate the improper integral ∫ from 0 to ∞ e^{-x} sin(x) dx.
Question 5

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Survive the Calculus Gauntlet: Fierce Foes Await

Quiz Intelligence

Quiz Questions

What is the radius of convergence of the power series sum from n=1 to infinity of (n! / n^n) x^n?

In the Maclaurin series expansion of ln(1 + x), the coefficient of the x^4 term is:

For the function f(x, y) = x^2 y + sin(x y), compute the mixed partial derivative f_{xy}(0, 0).

By Green's theorem, the counterclockwise line integral around the unit circle of -y dx + x dy equals:

Evaluate the improper integral ∫ from 0 to ∞ e^{-x} sin(x) dx.

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