Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
The problem asks us to identify which of the given improper integrals converges. A. $\int_{1}^{\inft...
Improper IntegralsConvergenceDivergenceIntegration Techniques
2025/4/23
The problem asks to differentiate the function $y = \sqrt{4x + 7}$ with respect to $x$.
CalculusDifferentiationChain RuleDerivatives
2025/4/23
We are asked to differentiate the function $y = \sqrt[3]{(ax+b)^2}$ with respect to $x$.
DifferentiationChain RuleDerivativesCalculus
2025/4/23
The problem asks to find the derivative of the function $y = \frac{1}{x}$ with respect to $x$.
DifferentiationPower RuleDerivativesCalculus
2025/4/23
The problem asks to find the derivative of the following two functions: a) $y = x \cdot \sin(2^{x+1}...
DerivativesProduct RuleChain RuleTrigonometric FunctionsExponential Functions
2025/4/22
The problem asks us to find the derivatives of the following two functions: a) $y = x\sin(2x+1)$ b) ...
DerivativesChain RuleProduct RuleTrigonometric FunctionsExponential Functions
2025/4/22
The problem consists of several calculus questions. We are asked to: a. Find the tangent plane to $z...
CalculusMultivariable CalculusTangent PlaneSeries ConvergenceP-SeriesRatio TestLaplacianNumerical IntegrationMid-ordinate RuleSimpson's RuleRelative ErrorPartial DerivativesPower SeriesRadius of Convergence
2025/4/22
Solve the inequality $\cos(\frac{1}{2}\theta - \frac{\pi}{3}) \le \frac{1}{\sqrt{2}}$.
TrigonometryInequalitiesTrigonometric InequalitiesIntervals
2025/4/22
The problem asks us to differentiate the function $y = \sqrt[3]{(ax+b)^2}$ with respect to $x$.
DifferentiationChain RuleDerivativesCalculus
2025/4/22
a. Find the equation of the tangent plane to $z = \ln(2x+y)$ at the point $(1, 2)$. b. Let $\sum_{x=...
Multivariable CalculusPartial DerivativesTangent PlaneInfinite Seriesp-seriesConvergence TestsIntegral Test
2025/4/21