Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
We are asked to evaluate several iterated integrals.
Iterated IntegralsMultivariable CalculusIntegration
2025/5/18
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
2025/5/18
The problem asks us to solve the Cauchy problem, which is the initial value problem for the differen...
Differential EquationsCauchy ProblemInitial Value ProblemIntegration
2025/5/18
We are asked to solve the following differential equation: $\frac{y'}{\sin x} - y^3 = 0$.
Differential EquationsSeparation of VariablesIntegration
2025/5/18
The problem asks us to solve a first-order linear differential equation using Bernoulli's method. Th...
Differential EquationsBernoulli EquationFirst-Order Differential EquationsSolution Methods
2025/5/18
We are asked to solve the differential equation $xy' + y = x^3$.
Differential EquationsFirst-Order Linear Differential EquationIntegration
2025/5/18
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
2025/5/18
The image contains several mathematics problems. We will solve problem number 8 which asks us to fin...
IntegrationPartial FractionsCalculusDefinite Integral
2025/5/18
The problem asks to prove the formula for the Fourier coefficient $b_n$ given the Fourier series exp...
Fourier SeriesOrthogonalityIntegration
2025/5/18
The problem states that a function $f(x)$ is defined on an open interval $(-L, L)$ and has period $2...
Fourier SeriesOrthogonalityIntegration
2025/5/18