Analysis

Problems related to calculus, limits, series, etc.

Problems in this category

Evaluate the double integral $\iint_S x \, dA$, where $S$ is the region between the curves $y = x$ a...

Double IntegralsRegion of IntegrationCalculusIntegration

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

Double IntegralsMultivariable CalculusIntegrationAreaTrigonometric FunctionsLogarithmic Functions

We are asked to evaluate six iterated integrals.

Iterated IntegralsDouble IntegralsCalculus

We are asked to evaluate several iterated integrals.

Iterated IntegralsMultivariable CalculusIntegration

The problem states that we have a function $f_a(x) = x^3 - 1 - a(x-1)$ and its graph $C_a$ depending...

CalculusFunctionsDerivativesTangentsCurve sketchingPolynomials

The problem asks us to solve the Cauchy problem, which is the initial value problem for the differen...

Differential EquationsCauchy ProblemInitial Value ProblemIntegration

We are asked to solve the following differential equation: $\frac{y'}{\sin x} - y^3 = 0$.

Differential EquationsSeparation of VariablesIntegration

The problem asks us to solve a first-order linear differential equation using Bernoulli's method. Th...

Differential EquationsBernoulli EquationFirst-Order Differential EquationsSolution Methods

We are asked to solve the differential equation $xy' + y = x^3$.

Differential EquationsFirst-Order Linear Differential EquationIntegration

We are given the differential equation $y'' + 3y' + 2y = \frac{x-1}{x^2}e^{-x}$ (E). 1. We need to ...

Differential EquationsSecond OrderLinear Differential EquationsParticular SolutionHomogeneous Equation

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