Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
We are given the function $f(x) = (x+1)(x+2)(x+3)...(x+100)$. We need to find the derivative of $f(x...
DifferentiationDerivativesProduct RuleLimitsFactorials
2025/7/15
We need to evaluate the definite integral $I = \int_{-4}^{0} \frac{1}{\sqrt{4-x}} dx$.
Definite IntegralSubstitutionIntegration TechniquesCalculus
2025/7/14
We are given the equation $\int \frac{1}{tan(y)} dy = \int x dx$ and asked to solve it.
IntegrationTrigonometric FunctionsIndefinite IntegralsDifferential Equations
2025/7/12
We need to evaluate the limit of the expression $\frac{x-3}{1-\sqrt{4-x}}$ as $x$ approaches $3$.
LimitsCalculusIndeterminate FormsConjugateAlgebraic Manipulation
2025/7/11
We need to evaluate the limit: $\lim_{x\to 3} \frac{x-3}{1 - \sqrt{4-x}}$.
LimitsIndeterminate FormsConjugateRationalization
2025/7/11
We are asked to find the limit of the function $\frac{2x^2 + 3x + 4}{x-1}$ as $x$ approaches 1 from ...
LimitsCalculusFunctions
2025/7/8
The problem asks us to sketch the graphs of two functions: (1) $y = x\sqrt{4-x^2}$ (2) $y = e^{-x} +...
GraphingCalculusDerivativesMaxima and MinimaConcavityInflection PointsDomainSymmetry
2025/7/3
The problem asks to sketch the graph of the function $y = x\sqrt{4 - x^2}$.
CalculusFunction AnalysisDerivativesGraphingDomainCritical PointsLocal Maxima/MinimaOdd Functions
2025/7/3
We are asked to find the sum of the series $\frac{1}{2^2-1} + \frac{1}{4^2-1} + \frac{1}{6^2-1} + \d...
SeriesSummationPartial FractionsTelescoping Series
2025/7/3
The problem asks to evaluate several natural logarithm expressions. The expressions are: 1. $ln(\fra...
LogarithmsNatural LogarithmExponentsLogarithmic Properties
2025/7/3