Analysis

Problems related to calculus, limits, series, etc.

Problems in this category

We are asked to analyze the iterated integral $\int_0^2 \int_0^x k \, dy \, dx$. The goal is to sket...

Double IntegralsCenter of MassDensityIterated IntegralsCalculusMultivariable Calculus

The problem asks to calculate the area under the curve of the given functions between the specified ...

CalculusIntegrationDefinite IntegralArea under a curve

The problem defines a sequence $f$ such that for all $n \in \mathbb{N}$, $2f(n+1) + f(n) = 0$, and $...

Sequences and SeriesGeometric SequencesConvergenceLimits

The problem asks to evaluate the integral $\int 2^x dx$. The given solution is $\frac{2^{x+1}}{x+1} ...

IntegrationExponentialsDerivativesCalculus

We are asked to evaluate the limit: $\lim_{x \to 4} \frac{x-4}{x^2-16}$.

LimitsCalculusAlgebraic ManipulationRational Functions

The problem is to evaluate the following expression: $\frac{sin(\frac{2\pi}{3}) + cos(\frac{\pi}{4})...

TrigonometryTrigonometric FunctionsExpression EvaluationSimplificationRationalization

We need to evaluate the double integral $\iint_S \frac{2}{1+x^2} dA$, where $S$ is the triangular re...

Double IntegralsIntegrationCalculusMultivariable CalculusarctanIntegration by Parts

We need to evaluate the double integral $\int_{1}^{2} \int_{0}^{x^2} \frac{y^2}{x} \, dy \, dx$.

Double IntegralIntegration

We are asked to evaluate the iterated integral $\int_{0}^{2} \int_{-x}^{x} e^{-x^2} dy dx$.

Iterated IntegralsCalculusIntegrationDefinite IntegralsSubstitution

The problem asks to evaluate the limit $\lim_{x \to \infty} (\sqrt{x^2+x} - \sqrt{x^2-1})$.

LimitsCalculusRationalizationSquare Roots

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