Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
The problem asks us to evaluate four limits based on the provided graph of a function $f(x)$. The li...
LimitsFunctionsGraph AnalysisOne-sided Limits
2025/6/28
The problem asks us to evaluate three limits, $A$, $B$, and $C$. $A = \lim_{x\to1} \frac{1+x}{\sqrt{...
LimitsCalculusIndeterminate FormsRationalizationL'Hopital's Rule (implied)
2025/6/28
The problem asks us to find the surface area of the solid generated by revolving the curve $y = x^{3...
CalculusSurface AreaSolid of RevolutionIntegrationDefinite IntegralApproximation
2025/6/28
The problem asks to find the volume of the solid generated by revolving the region bounded by the cu...
CalculusVolume of RevolutionIntegrationWasher Method
2025/6/28
The problem provides a function $f(x) = -x + 4 + \ln(\frac{x+1}{x-1})$ defined on the interval $(1, ...
LimitsDerivativesAsymptotesFunction AnalysisTangent LinesLogarithmic Functions
2025/6/28
Find the derivative of the function $g(x) = x^2 - 8\ln{x} - 1$.
CalculusDifferentiationDerivativesLogarithmic Functions
2025/6/28
We are asked to evaluate two integrals using the given substitutions. The integrals are: (a) $\int \...
IntegrationSubstitutionDefinite IntegralsIndefinite IntegralsCalculus
2025/6/27
We are given a set of statements about basic concepts in calculus and asked to determine if they are...
CalculusDerivativesAntiderivativesLocal ExtremaIncreasing/Decreasing FunctionsDifferentiabilityCritical PointsMean Value Theorem
2025/6/27
The problem asks to find the domain of the function $f(x) = \sqrt{1 - \frac{x+13}{x^2+4x+3}}$ and to...
DomainContinuityInequalitiesRational FunctionsLimits
2025/6/27
## 1. Problem Description
DomainContinuityFunctionsSquare RootGreatest Integer FunctionInequalities
2025/6/27