Expert-Level Calculus Quiz: Five Tough Problems
A set of five high-difficulty calculus questions designed to challenge seasoned mathematicians.
Quiz Questions
Answer all questions below and test your knowledge.
- 1
Evaluate the limit as (x,y)→(0,0) of (x^2 y) / (x^4 + y^2).
- 2
Compute the integral ∫₀^{π/2} ln(sin x) dx.
- 3
Determine whether the series Σ_{n=1}^∞ (-1)^{n+1} / (n^{3/2}) converges absolutely, conditionally, or diverges.
- 4
Find the particular solution of y'' - 4y' + 4y = e^{2x} that satisfies y(0)=1 and y'(0)=0.
- 5
What is the curvature of the graph y = sin x at the point where x = π/2?
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