Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
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
We are given the graph of a function $h(x)$ and we are asked to find the value of $h(-4)$ and $h^{-1...
FunctionsInverse FunctionsGraph Interpretation
2025/3/9
The problem asks whether the function $g(x) = x^3$, whose graph is provided, has an inverse.
Inverse FunctionsOne-to-one FunctionsHorizontal Line Test
2025/3/9
We are asked to evaluate the indefinite integral $\int (5x^4 - 3x^2 + \frac{3\sqrt{x}}{2}) dx$.
Indefinite IntegralsPower RulePolynomialsCalculus
2025/3/9