Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
The problem presents a sequence: $\sin 1, 2 \sin \frac{1}{2}, 3 \sin \frac{1}{3}, 4 \sin \frac{1}{4}...
SequencesLimitsTrigonometry
2025/5/27
The problem asks us to find an explicit formula $a_n$ for the given sequence, determine whether the ...
SequencesLimitsConvergenceExplicit Formula
2025/5/27
The problem asks us to analyze the sequence $a_n = e^{-n} \sin n$. We need to find the first few ter...
SequencesLimitsConvergenceSqueeze TheoremTrigonometric FunctionsExponential Functions
2025/5/27
The problem asks us to analyze the sequence $a_n = e^{-n} \sin n$. We need to find the first few ter...
SequencesLimitsTrigonometryExponential FunctionsSqueeze TheoremConvergence
2025/5/27
The problem asks us to analyze several sequences given by their explicit formulas. For each sequence...
SequencesLimitsConvergenceDivergenceL'Hopital's Rule
2025/5/27
The problem requires us to find the first five terms of the given sequences $\{a_n\}$, determine if ...
SequencesLimitsConvergenceDivergence
2025/5/27
We need to find the limit of the expression $\frac{x \sin(3x)}{\sin^2(5x)}$ as $x$ approaches 0. Th...
LimitsTrigonometric FunctionsL'Hopital's Rule
2025/5/27
The problem asks to evaluate the limit: $A = \lim_{x\to 0} \frac{\ln(1+x)}{\sin x}$.
LimitsL'Hopital's RuleTrigonometric FunctionsLogarithmic Functions
2025/5/27
The problem asks to evaluate the definite integral $\int_{0}^{1} x\sqrt{x^2+1} dx$.
Definite Integralu-substitutionIntegration TechniquesCalculus
2025/5/26
The problem asks us to evaluate several definite integrals. Here, we will solve the first 4 problems...
Definite IntegralsPower RuleIntegrationAntiderivatives
2025/5/26