Analysis

Problems related to calculus, limits, series, etc.

Problems in this category

The problem asks us to construct the Fourier series of the function $f(x) = x$ on the interval $-\pi...

Fourier SeriesTrigonometric FunctionsIntegrationCalculus
2025/5/13

The problem seems to involve analysis of a function $f(x) = -x - \frac{4}{x}$. It asks about limits ...

Function AnalysisDerivativesLimitsDomainInequalities
2025/5/13

From what I can decipher, the problem involves analyzing a function $f(x) = -x - \frac{4}{x}$ and an...

LimitsDerivativesAsymptotesFunction Analysis
2025/5/13

The image appears to present several math problems related to limits, derivatives, and inequalities....

LimitsDerivativesInequalitiesFunction AnalysisCalculus
2025/5/13

The problem seems to ask to find the derivative of the function $y = f(x) = \ln(x + \sqrt{1+x^2})$.

CalculusDifferentiationChain RuleLogarithmic FunctionsDerivatives
2025/5/13

The problem asks us to evaluate the definite integral: $A(R) = \int_{-3}^1 (\frac{4-\sqrt{4-4y}}{2} ...

Definite IntegralIntegration TechniquesSubstitutionCalculus
2025/5/12

Given the function $g(x) = 3x^4 - 2x^2 + 49$, we need to find the first and second derivatives, $g'(...

CalculusDerivativesFirst DerivativeSecond DerivativeSign AnalysisPolynomial Functions
2025/5/12

The problem asks us to evaluate the definite integral of the polynomial $x^2 - 3x + 5$ from $2$ to $...

Definite IntegralIntegrationPolynomialCalculus
2025/5/12

The problem asks us to evaluate the definite integral of $x^2 - 3x$ from 1 to 2, and subtract from t...

Definite IntegralIntegrationCalculus
2025/5/12

The problem asks to evaluate the definite integral $\int_{1}^{2} (x^2 - 3x) \, dx + \int_{1}^{2} (x^...

Definite IntegralIntegrationCalculus
2025/5/12