Advanced Calculus Test
Test of advanced calculus concepts through seven demanding multiple-choice items.
Quiz Questions
Answer all questions below and test your knowledge.
- 1
Compute the improper integral ∫_{1}^{∞} 1/x^2 dx.
- 2
Solve dy/dx = y^2 with y(0)=1. Which expression describes y(x)?
- 3
What is the limit of sin(x)/x as x approaches zero?
- 4
The infinite series Σ_{n=1}^{∞} 1/n^2 converges to which constant?
- 5
For the power series Σ_{n=0}^{∞} n! x^n, what is the radius of convergence?
- 6
Evaluate the line integral of F(x,y) = (y, x) along the straight segment from (0,0) to (1,1).
- 7
What is ∫_{0}^{1}∫_{0}^{1} e^{x+y} dx dy ?
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