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: 20

2017 ASDAN Math Tournament, 1
Tags: 2017 , Calculus Test
Compute $$\int_0^13x^2dx.$$

2017 ASDAN Math Tournament, 4
Tags: 2017 , Calculus Test
A ladder $10\text{ m}$ long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of $1\text{ m/s}$, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is $6\text{ m}$ from the wall?

2016 ASDAN Math Tournament, 9
Tags: 2016 , Calculus Test
Compute $$\int_0^\infty\frac{\ln\left(\frac{1+x^{11}}{1+x^3}\right)}{(1+x^2)\ln x}dx.$$

2016 ASDAN Math Tournament, 6
Tags: 2016 , Calculus Test
For what positive value $k$ does the equation $\ln x=kx^2$ have exactly one solution?

2016 ASDAN Math Tournament, 10
Tags: 2016 , Calculus Test
Using the fact that $$\sum_{n=1}^\infty\frac{1}{n^2}=\frac{\pi^2}{6},$$ compute $$\int_0^1(\ln x)\ln(1-x)dx.$$

2016 ASDAN Math Tournament, 5
Tags: 2016 , Calculus Test
Find $$\lim_{x\rightarrow0}\frac{\sin(x)-x}{x\cos(x)-x}.$$

2016 ASDAN Math Tournament, 3
Tags: 2016 , Calculus Test
If $f(x)=e^xg(x)$, where $g(2)=1$ and $g'(2)=2$, find $f'(2)$.

2017 ASDAN Math Tournament, 6
Tags: 2017 , Calculus Test
Compute $$\lim_{x\rightarrow0}\frac{\sqrt[5]{\cos x}-\sqrt[3]{\cos x}}{x^2}.$$

2016 ASDAN Math Tournament, 7
Tags: 2016 , Calculus Test
Compute $$\int_0^{\frac{\pi}{2}}\frac{e^x(\sin x+\cos x-2)}{(\cos x-2)^2}dx.$$

2017 ASDAN Math Tournament, 9
Tags: 2017 , Calculus Test
Compute $$\int_0^4\frac{x^4-4x+4}{1+2017^{x-2}}dx.$$

2016 ASDAN Math Tournament, 4
Tags: 2016 , Calculus Test
The radius $r$ of a circle is increasing at a rate of $2$ meters per minute. Find the rate of change, in $\text{meters}^2/\text{minute}$, of the area when $r$ is $6$ meters.

2017 ASDAN Math Tournament, 8
Tags: 2017 , Calculus Test
Compute $$\int_0^1\frac{2xe^x-1}{2x^2e^x+2}dx.$$

2017 ASDAN Math Tournament, 10
Tags: 2017 , Calculus Test
Compute $$\lim_{k\rightarrow\infty}\left(\frac{2017^{1/k}}{k+1}+\frac{2017^{2/k}}{k+\frac{1}{2}}+\dots+\frac{2017^{k/k}}{k+\frac{1}{k}}\right).$$

2017 ASDAN Math Tournament, 3
Tags: 2017 , Calculus Test
Let $f(x)=x^4+2x+1$. Find the slope of the tangent line to the curve at $(0,1)$.

2016 ASDAN Math Tournament, 1
Tags: 2016 , Calculus Test
Let $f(x)=(x-1)^3$. Find $f'(0)$.

2017 ASDAN Math Tournament, 5
Tags: 2017 , Calculus Test
Compute the maximum value attained by $f(x)=x^{1/x^2}$.

2016 ASDAN Math Tournament, 8
Tags: 2016 , Calculus Test
Let $f$ be a differentiable function such that $f'(0)=4$ and $f(0)=3$. Compute $$\lim_{x\rightarrow\infty}\left(\frac{f\left(\frac{1}{x}\right)}{f(0)}\right)^x.$$

2016 ASDAN Math Tournament, 2
Tags: 2016 , Calculus Test
Suppose $a$ and $b$ are two variables that satisfy $\textstyle\int_0^2(-ax^2+b)dx=0$. What is $\tfrac{a}{b}$?

2017 ASDAN Math Tournament, 7
Tags: 2017 , Calculus Test
Compute $$\lim_{t\rightarrow0}\int_0^t\frac{x^2+4x+4}{\sqrt{t^2-x^2}}dx.$$

2017 ASDAN Math Tournament, 2
Tags: 2017 , Calculus Test
Let $f(x)=x^2$ and let $g(x)=x+1$. Let $h(x)=f(g(x))$. Compute $h'(1)$.