Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
We are asked to find $\frac{\partial w}{\partial t}$ using the chain rule for the given functions in...
Multivariable CalculusChain RulePartial Derivatives
2025/5/10
The problem asks us to prove that the product of two even functions is even, and the product of two ...
Even FunctionsOdd FunctionsFunction PropertiesProof
2025/5/9
The problem provides the Fourier series expansion of a function $f(x)$ defined on the interval $(-L,...
Fourier SeriesOrthogonalityIntegration
2025/5/9
The problem states that if a function $f(x)$ is defined in an open interval $(-L, L)$ and has period...
Fourier SeriesOrthogonalityIntegrationTrigonometric Functions
2025/5/9
We are asked to find the Fourier series of the function $f(x)$ defined as: $f(x) = \begin{cases} 2, ...
Fourier SeriesTrigonometric SeriesIntegration
2025/5/9
We want to find the Laplace transform of $F(t) = \sin(kt)$.
Laplace TransformIntegration by PartsTrigonometric FunctionsDefinite Integrals
2025/5/9
Find the Laplace transform of the function $F(t) = \sin(kt)$.
Laplace TransformIntegrationTrigonometric FunctionsCalculus
2025/5/9
The problem asks us to find the Fourier series representation of the function $f(x)$ defined as: $f(...
Fourier SeriesIntegrationTrigonometric Functions
2025/5/9
The problem asks us to find the derivatives of two functions. i. $3x + y^3 - 4y = 10x^2$ ii. $y = \...
DifferentiationImplicit DifferentiationChain RuleDerivatives
2025/5/9
We are asked to compute the definite integral $\int_{0}^{4} f(x) dx$ for the function $f(x) = 4x^3 -...
Definite IntegralIndefinite IntegralIntegrationCalculus
2025/5/9