This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 6

2017 ASDAN Math Tournament, 3
Tags: 2017 , Calculus Tiebreaker
Compute $$\int_0^1\frac{x^{2017}-1}{\log x}dx.$$

2016 ASDAN Math Tournament, 1
Tags: 2016 , Calculus Tiebreaker
Compute $$\lim_{x\rightarrow1}\frac{x^3-1}{x-1}.$$

2016 ASDAN Math Tournament, 2
Tags: 2016 , Calculus Tiebreaker
Consider the curves with equations $x^n+y^n=1$ for $n=2,4,6,8,\dots$. Denote $L_{2k}$ the length of the curve with $n=2k$. Find $\lim_{k\rightarrow\infty}L_{2k}$.

2016 ASDAN Math Tournament, 3
Tags: 2016 , Calculus Tiebreaker
Compute $$\int_0^\pi\frac{1-\sin x}{1+\sin x}dx.$$

2017 ASDAN Math Tournament, 1
Tags: 2017 , Calculus Tiebreaker
Compute $$\int_0^6\frac{x-3}{x^2-6x-7}dx.$$

2017 ASDAN Math Tournament, 2
Tags: 2017 , Calculus Tiebreaker
Let $f$ be a linear function. Compute the slope of $f$ if $$\int_3^5f(x)dx=0\text{ and }\int_5^7f(x)dx=12.$$