Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
We need to evaluate the definite integral: $\int_{0}^{+\infty} \frac{e^{ax} - e^{bx}}{(1 + e^{ax})(1...
Definite IntegralCalculusIntegration TechniquesExponential Functions
2025/4/12
We need to evaluate the definite integral $$ \int_{0}^{+\infty} \frac{e^{ax} - e^{bx}}{(1+e^{ax})(1+...
Definite IntegralIntegration TechniquesSubstitutionCalculus
2025/4/12
We are asked to evaluate the definite integral $$ \int_{0}^{+\infty} \frac{e^{ax} - e^{bx}}{(1+e^{ax...
Definite IntegralIntegrationCalculusExponential Functions
2025/4/12
We are asked to evaluate the integral $$ \int_{0}^{+\infty} \frac{[W(x)]^2}{x^2\sqrt{x}} dx $$ where...
Definite IntegralLambert W functionGamma functionIntegration by substitutionCalculus
2025/4/12
We need to evaluate the definite integral: $\int_{0}^{+\infty} \frac{[W(x)]^2}{x^2\sqrt{x}} dx$, whe...
Definite IntegralLambert W functionGamma FunctionIntegration by SubstitutionDivergence
2025/4/12
We need to evaluate the definite integral from $0$ to $+\infty$ of the function $\frac{[W(x)]^2}{x^2...
Definite IntegralLambert W functionSubstitutionGamma Function
2025/4/12
We are asked to evaluate the definite integral $\int_{0}^{\frac{\pi}{6}} \frac{\sin x \sin(x + \frac...
Definite IntegralTrigonometric IdentitiesSubstitutionIntegration Techniques
2025/4/12
The problem has two parts. Part (a) asks to determine the truthfulness of two statements and provide...
CalculusExtreme ValuesRolle's TheoremHyperbolic Functions
2025/4/12
The problem asks us to determine whether two statements about differentiability and continuity are t...
DifferentiabilityContinuityLimitsReal AnalysisContrapositive
2025/4/11
The problem asks us to find the domain of the function $f(x) = \frac{\sqrt{(\sqrt{x})^x - x^{\sqrt{x...
DomainFunctionsLogarithmsExponentsInequalities
2025/4/11