Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
We are asked to evaluate the definite integral $\int_0^1 x(1+x)^{2022} dx$.
Definite IntegralIntegration by SubstitutionPower Rule
2025/3/21
We are given the function $g(x) = x^2 - 1 + \ln x$ defined on the interval $]0, +\infty[$. We need t...
CalculusDerivativesFunction AnalysisMonotonicityLogarithmic Functions
2025/3/20
The problem asks us to evaluate the integral $\int \frac{1}{\sin x - \cos x} dx$.
IntegrationTrigonometric FunctionsSubstitutionCalculus
2025/3/19
Find the value of $\alpha$ given that $\sin{\alpha} = 1$.
TrigonometrySine FunctionSolving EquationsRadians
2025/3/19
The problem asks to evaluate the expression $\cos\frac{9\pi}{4} + \tan(-\frac{11\pi}{6})$.
TrigonometryTrigonometric FunctionsAngle ConversionEvaluation
2025/3/19
Find the maximum and minimum values of the function $f(x) = 5 - \sin x$.
TrigonometryFunction AnalysisMaximum and Minimum ValuesSine FunctionRange of a Function
2025/3/19
The problem asks to find the minimum positive period of the function $f(x) = 4\sin(4x + \frac{\pi}{5...
TrigonometryPeriodic FunctionsSine FunctionPeriod
2025/3/19
The problem asks us to find the interval where the function $f(x) = \cos(\frac{\pi}{4} - x)$ is mono...
TrigonometryMonotonicityIntervalsCalculus
2025/3/19
The problem asks us to evaluate the definite integral $\int_{0}^{1} \log(x^2 + 1) \, dx$.
Definite IntegralIntegration by PartsLogarithmsTrigonometric FunctionsCalculus
2025/3/18
We are asked to solve the integration: $\int \frac{1}{\sin x - \cos x} dx$.
IntegrationTrigonometric IntegralsCalculusDefinite Integrals
2025/3/17