Advanced Calculus Test – Master Hard Concepts
Five demanding multiple‑choice items that probe deep understanding of core calculus topics.
Quiz Questions
Answer all questions below and test your knowledge.
- 1
Determine the limit as x approaches 0 of (e^{2x} - 1 - 2x) / x^2.
- 2
Which series converges among the following choices?
- 3
Compute the double integral over the unit square of (x^2 + y^2) with respect to area.
- 4
For f(x)=ln(1+x), which bound correctly estimates the remainder R_3(x) on 0\le x\le 0.5?
- 5
What is the value of the improper integral \int_{1}^{\infty} \frac{1}{x(\ln x)^2}\,dx?
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