Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
The problem asks to express the definite integral $\int_0^3 (x-16) dx$ as a limit of Riemann sums, u...
Definite IntegralsRiemann SumsCalculus
2025/5/10
The problem states that if $w = f(r-s, s-t, t-r)$, then we need to show that $\frac{\partial w}{\par...
Partial DerivativesChain RuleMultivariable Calculus
2025/5/10
We are given the equation $3x^2z + y^3 - xyz^3 = 0$ and we need to find the partial derivative of $z...
Partial DerivativesImplicit DifferentiationMultivariable CalculusChain RuleProduct Rule
2025/5/10
We need to find $\frac{dy}{dx}$ for the given implicit equations.
Implicit DifferentiationCalculusDerivatives
2025/5/10
We are given the graph of a function $g$. We need to: 1) Determine the domain $D_g$ of the function ...
Function AnalysisDomainFunction PropertiesOdd FunctionGraphingSymmetry
2025/5/10
The problem involves analyzing the function $f(x) = \frac{x}{x^2-1}$. We need to determine the domai...
Function AnalysisDomainOdd FunctionFunction VariationsMonotonicityDerivatives
2025/5/10
The problem asks us to solve several trigonometric equations and inequalities within specified inter...
TrigonometryTrigonometric EquationsTrigonometric InequalitiesIntervals
2025/5/10
The problem asks us to prove the formulas for the Fourier coefficients $a_n$ and $b_n$ given the Fou...
Fourier SeriesOrthogonalityIntegrationTrigonometric Functions
2025/5/10
The problem describes a function $f(x) = 1 - x \ln x$. It asks to find the domain of the function, c...
CalculusFunctionsLimitsDerivativesAsymptotesDomainTable of VariationsIntersection of Curves
2025/5/10
The problem asks to find $\frac{\partial w}{\partial t}$ using the chain rule, where $w = \sqrt{x^2 ...
Partial DerivativesChain RuleMultivariable Calculus
2025/5/10