Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
We are asked to differentiate the function $y = \frac{4x^2 + 3}{x^2 + 1}$ with respect to $x$.
CalculusDifferentiationQuotient Rule
2025/3/11
The problem is to evaluate the definite integral $\int_{0}^{\frac{\pi}{2}} \frac{\cos x}{1 + \sin x}...
Definite IntegralSubstitutionLogarithm
2025/3/11
We need to find the indefinite integral of the function $e^{2x}\sin{x}$.
IntegrationIntegration by PartsTrigonometric FunctionsExponential FunctionsIndefinite Integral
2025/3/11
We are asked to evaluate the infinite sum $\sum_{n=1}^{\infty} n (\frac{1}{3})^n$.
Infinite SeriesDifferentiationGeometric Series
2025/3/10
We are asked to determine whether the series $\sum_{n=1}^{\infty} \frac{\sqrt{2n+1}}{n^2}$ converges...
Series ConvergenceLimit Comparison Testp-series
2025/3/10
Determine whether the series $\sum_{n=1}^{\infty} \frac{3n+1}{n^3 - 4}$ converges or diverges.
Series ConvergenceLimit Comparison TestInfinite Series
2025/3/10
The problem consists of three parts: 1. Sketch the graph of the relation $R = A \times B$ for given...
FunctionsDomainRelations
2025/3/10
The problem asks to find $y'$ (the derivative of $y$ with respect to $x$) for two equations: a) $x^y...
DifferentiationImplicit DifferentiationTranscendental Functions
2025/3/10
The problem asks to find the value of the infinite sum $\sum_{n=1}^{\infty} \frac{n^3}{(2n)!}$.
Infinite SeriesTaylor SeriesSummationHyperbolic Functions
2025/3/10
We are asked to determine if the series $\sum_{n=1}^{\infty} \frac{5^n}{n^5}$ converges or diverges.
Infinite SeriesConvergenceDivergenceRatio TestLimits
2025/3/10