Analysis

Problems related to calculus, limits, series, etc.

Problems in this category

The problem asks to evaluate the definite integral $K = \int_{0}^{\pi} x \sin x \, dx$.

Definite IntegralIntegration by PartsTrigonometric Functions

We are asked to evaluate the definite integral $I = \int_{0}^{4} xe^{x^2} dx$.

Definite Integralu-substitutionIntegration

We need to evaluate the definite integral $I = \int_{0}^{2} (x + 1 + \frac{3}{x+1}) dx$.

Definite IntegralIntegrationAntiderivativeCalculus

The problem asks us to find the sum of the series $\sum_{n=1}^{\infty} \frac{x^n}{3^n}$.

SeriesGeometric SeriesConvergenceSummation

The problem asks to find the derivatives of two expressions: a) $x^4 - 3x^2 + 4x - 1$ b) $\frac{2x+3...

CalculusDifferentiationDerivativesPower RuleQuotient Rule

The problem is to find the derivative of the function $f(x) = \cos(x) \cdot e^x$.

CalculusDifferentiationProduct RuleTrigonometric FunctionsExponential Functions

The problem asks to calculate the derivatives of the following three expressions: a) $x^4 - 3x^2 + 4...

DerivativesCalculusPower RuleQuotient RuleProduct RulePolynomialsTrigonometric FunctionsExponential Functions

We need to find the value of the infinite sum $\sum_{n=1}^{\infty} (-1)^{n+1} \frac{2^n}{n!}$.

Infinite SeriesTaylor SeriesExponential FunctionSummation

We need to find the sum of the series $\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n(n+1)}$.

Infinite SeriesPartial FractionsAlternating SeriesConvergenceLogarithms

We are asked to determine whether the series $\sum_{n=1}^{\infty} (-1)^{n+1} \frac{n}{n^2+1}$ conver...

SeriesConvergenceDivergenceAlternating Series TestLimit Comparison TestAbsolute ConvergenceConditional Convergence

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