Mathematics & Logic

Gauntlet of Advanced Calculus: 9 Trials

Nine ferocious questions probing the depths of calculus, from series convergence to line integrals.

#improper integrals#multivariable calc#power series#advanced calculus#Green theorem#Stokes theorem#parametric derivatives#LHopital applications#Taylor polynomials

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Total Questions

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hard

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Quiz Questions

Answer all questions below and test your knowledge.

1
Find the third-degree Taylor polynomial of f(x)=cos(x) at x=0.
Question 1
2
Evaluate lim_{x→0} (e^x - 1 - x)/x^2 using L'Hôpital's rule.
Question 2
3
Determine if ∫_1^∞ sin(x)/x dx converges.
Question 3
4
For x=sin(t), y=cos(t), compute d^2y/dx^2 at t=π/2.
Question 4
5
Compute ∂/∂x [x y e^{x y}] where y constant.
Question 5
6
∫ x^2 e^x dx by parts twice.
Question 6
7
Radius of convergence for ∑_{n=0}^∞ x^n / (n! 2^n).
Question 7
8
By Green's theorem, ∮_C (x-y) dx + (x+y) dy for unit circle C.
Question 8
9
Stokes' theorem: ∫_C F·dr = ∬_S curl F · dS for F=( -y, x, z), S unit sphere upper? Simplify: for circle in xy-plane.
Question 9