Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
We are given a sequence $(u_n)$ defined by the recurrence relation $u_n = -\frac{1}{3}u_{n-1} + 1$ w...
SequencesRecurrence RelationsLimitsGeometric SequencesSeries
2025/3/27
The image contains a set of mathematical problems related to a function $f(x)$. The tasks include ca...
CalculusDerivativesFunction AnalysisAsymptotesInverse FunctionsTangentsGraphingIntegrationArea Calculation
2025/3/27
The problem is based on the function $f(x) = 1 - x - e^x$. It involves calculating limits, finding ...
LimitsDerivativesInverse FunctionsAsymptotesFunction AnalysisCalculus
2025/3/27
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