Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
We are asked to determine whether the series $\sum_{n=1}^\infty (-1)^{n+1} \frac{\ln n}{n}$ converge...
Series ConvergenceAlternating Series TestLimitsL'Hopital's RuleDerivativesMonotonicity
2025/3/12
The problem asks to evaluate the expression $\cos(\frac{4\pi}{3}) - \sin(\frac{4\pi}{3})$.
TrigonometryTrigonometric FunctionsAngle CalculationUnit Circle
2025/3/12
The problem is to evaluate the definite integral $I = \int_{0}^{\infty} \frac{\sin(x)}{x} dx$.
Definite IntegralLaplace TransformImproper IntegralTrigonometric FunctionsIntegration Techniques
2025/3/12
The problem asks to evaluate the definite integral $I = \int_{0}^{\infty} \frac{\sin(x)}{x} dx$. Thi...
Definite IntegralImproper IntegralLaplace TransformIntegrationTrigonometric Functions
2025/3/12
We need to solve the inequality $\sqrt{(a-3)^2} \sin a - 3 < 0$.
InequalitiesTrigonometryAbsolute ValueFunctionsSolution of Inequalities
2025/3/11
The problem provides the definition of the generating function $W^{(s)}(x, t)$ for the higher-order ...
Generating FunctionsFibonacci PolynomialsSeriesComplex NumbersGeometric Series
2025/3/11
We are asked to find the area of the region bounded by the graphs of $x = \pm \sqrt{y-2}$ and $x = y...
CalculusIntegrationArea between curvesDefinite IntegralsQuadratic Equations
2025/3/11
The problem asks us to find the area of the region bounded by the curves $x = y^2 - 2$ and $x = y - ...
CalculusIntegrationArea between curvesDefinite Integrals
2025/3/11
We need to solve the second-order homogeneous linear differential equation $26y'' - 2y' + y = 0$.
Differential EquationsSecond-Order Differential EquationsHomogeneous Differential EquationsComplex RootsLinear Differential Equations
2025/3/11
We want to evaluate the integral $\int \frac{x^2 + 72}{(x \sin x + 9 \cos x)^2} dx$.
IntegrationCalculusTrigonometryQuotient Rule
2025/3/11