Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
We are asked to evaluate the double integral $\iint_R f(x, y) dA$ where $R = \{(x, y): 1 \le x \le 4...
Double IntegralsMultivariable CalculusPiecewise Functions
2025/5/16
The problem asks us to evaluate two integrals: 1. $\int e^{2x} dx$
IntegrationCalculusDefinite IntegralsSubstitutionIntegration by Parts
2025/5/15
We are asked to evaluate the definite integral $\int_0^\pi \sin^2 x \, dx$.
Definite IntegralTrigonometric IdentityIntegrationSin^2(x)Calculus
2025/5/15
We are asked to find the critical points of the given functions and classify them as local maxima, l...
Multivariable CalculusPartial DerivativesCritical PointsLocal MaximaLocal MinimaDeterminantSecond Derivative Test
2025/5/15
The problem asks to find $y'$ given the equation $x^y = y^x$ using implicit differentiation.
Implicit DifferentiationDerivativesLogarithms
2025/5/15
The problem asks us to determine whether the given statements are true or false. If true, we must ex...
LogarithmsLimitsFunctionsReal AnalysisCounterexamples
2025/5/15
a) Determine if the statement "If $a, b \in \mathbb{R} \setminus \{0\}$, then $\ln(ab) = \ln a + \ln...
Real AnalysisLimitsLogarithmsFunctionsDomain and Range
2025/5/15
We are given four problems: a) Find $y'$ using implicit differentiation, given $x^y = y^x$. b) A man...
Implicit DifferentiationRelated RatesRolle's TheoremChain RuleDifferentiationLogarithms
2025/5/15
The problem presents a differential equation $\frac{dV}{dx} = -w(x)$. We are asked to solve this dif...
Differential EquationsIntegrationAntiderivatives
2025/5/15
The problem consists of two sub-problems: (4) Determine whether the function $f(x) = -x + 5$ defined...
Function PropertiesEven and Odd FunctionsPeriodic FunctionsTrigonometry
2025/5/14