Analysis

Problems related to calculus, limits, series, etc.

Problems in this category

We are asked to evaluate the definite integral $\int_{0}^{\frac{\pi}{4}} \frac{1}{\sin^2 x + 3 \cos^...

Definite IntegralTrigonometric FunctionsSubstitutionIntegration Techniques
2025/4/24

The problem asks to solve the second-order differential equation $y'' = 20x^3$.

Differential EquationsSecond-Order Differential EquationsIntegrationGeneral Solution
2025/4/24

The problem is to find the second derivative of the function $y = 20x^3$. We need to find $y''$.

DifferentiationPower RuleSecond DerivativeCalculus
2025/4/24

The problem is to solve the differential equation $y''' = 20x^3$.

Differential EquationsIntegration
2025/4/24

We are given a graph of a function and asked to find information about the reciprocal of this functi...

CalculusFunction AnalysisDerivativesAsymptotesMaxima and MinimaGraphing
2025/4/23

The problem asks us to find the vertical asymptote of the function $f(x) = \frac{2x}{x+3}$, and to d...

LimitsAsymptotesRational FunctionsCalculus
2025/4/23

The problem asks for the vertical asymptote of the function $f(x) = \frac{2x}{x+3}$ and the sign of ...

LimitsVertical AsymptotesRational FunctionsCalculus
2025/4/23

The problem asks us to determine what types of asymptotes the function $f(x) = \frac{3x^3 + 2x^2 + x...

AsymptotesRational FunctionsVertical AsymptotesOblique AsymptotesPolynomial Long Division
2025/4/23

The problem defines a function $f(x) = x + \frac{1}{x}$. It asks us to: 1. Determine the domain $D_...

FunctionsDomainOdd FunctionsCalculusDerivativesMonotonicityVariation Table
2025/4/23

The problem asks us to evaluate several integrals and then to perform a partial fraction decompositi...

IntegrationDefinite IntegralsPartial FractionsSubstitutionTrigonometric Functions
2025/4/23