Mathematics & Logic

Elite Calculus Puzzles: Prove Your Expertise

Challenge your advanced calculus knowledge through 10 demanding questions spanning core theorems and techniques.

#Taylor series#vector calculus#power series#advanced limits#Green theorem#Stokes theorem#partial derivatives#integral convergence

Total Questions

Difficulty Level

hard

Progress

0/0

Quiz Questions

Answer all questions below and test your knowledge.

1
Evaluate the limit: lim (x→0) [sin(3x)/x - 3 cos(2x)] using L'Hôpital's rule if necessary.
Question 1
2
lim_{x\to 0} \frac{\tan x - x}{x^3}
Question 2
3
Does ∫_1^∞ dx / (x ln x ln(ln x)) converge?
Question 3
4
Taylor series of f(x)=e^x sin x around 0, coefficient of x^3/3!
Question 4
5
For f(x,y)=x^2 y + sin(xy), ∂²f/∂x∂y at (0,0)
Question 5
6
∂f/∂y where f=xy + e^{x/y} , but careful domain. Better: f(x,y)=(x+y)^3, ∂²f/∂x∂y.
Question 6
7
Radius of convergence for ∑ (n! x^n)/n^n
Question 7
8
Standard: ∑ n^2 x^n , R=
Question 8
9
∫ x sin x dx by parts, indefinite.
Question 9
10
For parametric x=t^2, y=t^3, dy/dx at t=1.
Question 10