Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
We are asked to evaluate the definite integral $\int_{-1}^{3} (5x^2 - x - 4) dx$.
Definite IntegralIntegrationPower RuleAntiderivative
2025/5/12
We are asked to evaluate the definite integrals given in problems 17 and 19. Problem 17 is: $\int_{-...
Definite IntegralsTrigonometric FunctionsIntegration by SubstitutionIntegration Techniques
2025/5/12
The problem asks to find the derivative, $f'(x)$, of eight different functions, $f(x)$, using the de...
CalculusDifferentiationDerivativesLimitsFirst Principles
2025/5/12
We need to find the global maximum and minimum values of the given functions $f(x, y)$ on the set $S...
Multivariable CalculusOptimizationExtremaLagrange MultipliersBounded Region
2025/5/12
We are asked to find the critical points of the following three functions and classify them as local...
Multivariable CalculusCritical PointsLocal MaximaLocal MinimaSaddle PointsPartial Derivatives
2025/5/12
We are asked to find the critical points of several functions and classify them as local maxima, loc...
Multivariable CalculusCritical PointsSecond Derivative TestLocal MaximaLocal MinimaSaddle PointsPartial Derivatives
2025/5/12
The problem asks to find all critical points of the given functions, and determine whether they corr...
Multivariable CalculusPartial DerivativesCritical PointsLocal ExtremaDiscriminant
2025/5/12
The problem asks us to fill in the blanks in the statement: "If $f(x, y)$ attains a maximum value at...
Multivariable CalculusOptimizationMaxima and MinimaCritical PointsBoundary Points
2025/5/12
We are asked to find the critical points of the given functions and determine whether they correspon...
Multivariable CalculusCritical PointsSecond Derivative TestLocal ExtremaPartial Derivatives
2025/5/12
The problem provides a graph of a function $f$. We need to: 1. Determine the domain $D_f$ of the fun...
FunctionsDomainRangeGraph AnalysisFunction EvaluationPreimages
2025/5/11