Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
The problem asks to evaluate the integral: $\int \frac{x^{4037}}{(x^2 + 1)^{2020}} dx$
CalculusIntegrationTrigonometric SubstitutionDefinite Integrals
2025/3/27
We are asked to evaluate the following three definite integrals: $I = \int_{1}^{4} (\frac{2}{\sqrt{x...
Definite IntegralsIntegration TechniquesTrigonometric IdentitiesPolynomial Long Division
2025/3/27
The problem asks to estimate the instantaneous rate of change of the function $f(x) = x^3 + 4x^2 - 1...
CalculusDerivativesInstantaneous Rate of ChangePower RulePolynomials
2025/3/26
The problem asks to determine the average rate of change of the function $f(x) = 4(x+2)^2 + 1$ on th...
Average Rate of ChangeFunctionsCalculus
2025/3/26
The problem asks to estimate the instantaneous rate of change of the function $f(x) = x^3 + 4x^2 - 1...
DerivativesInstantaneous Rate of ChangePower Rule
2025/3/26
The problem asks to estimate the interval(s) on which the rate of change of the function $f(x) = 10x...
CalculusDerivativesRate of ChangeIncreasing/Decreasing FunctionsQuadratic Equations
2025/3/26
The problem is divided into two parts, A and B. Part A deals with the function $g(x) = -(x-1)^2 + 1 ...
CalculusFunctionsDerivativesLimitsAsymptotesMonotonicityBijectivityInverse Functions
2025/3/25
We are given a sequence $(u_n)$ defined by $u_0 = 9e$ and $u_{n+1} = 3\sqrt{u_n}$ for all $n \in \ma...
SequencesLogarithmsGeometric SequencesRecursive Sequences
2025/3/25
We are given a sequence $(u_n)$ defined by $u_0 = 1$ and $u_{n+1} = \frac{2u_n}{u_n+2}$ for all $n \...
SequencesSeriesConvergenceArithmetic SequencesLimits
2025/3/25
We are asked to solve the integral $\int \frac{e^x}{4(1+e^{2x})} dx$.
IntegrationSubstitutionCalculus
2025/3/25