Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
The problem is to evaluate the indefinite integral of the function $\sqrt{x} - \frac{1}{2}x + \frac{...
IntegrationIndefinite IntegralPower RuleCalculus
2025/4/27
We are asked to solve two integration problems. First, we need to evaluate $\int (2\sqrt{x} + 5x^{-1...
IntegrationDefinite IntegralsIndefinite IntegralsPower RuleExponential FunctionsLogarithmic Functions
2025/4/27
We are asked to solve the following integral: $\int \frac{\cos x}{\sin^3 x (1-\sin^2 x)^{5/2}} dx$
CalculusIntegrationTrigonometric FunctionsDefinite Integrals
2025/4/27
We are given Laplace's equation: $\frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y...
Partial DerivativesLaplace's EquationHarmonic FunctionMultivariable Calculus
2025/4/27
We are given the function $f(x, y) = 3e^{2x} \cos y$. We need to verify that $\frac{\partial^2 f}{\p...
Partial DerivativesMultivariable CalculusDifferentiationClairaut's Theorem
2025/4/27
The problem asks us to verify that the mixed partial derivatives are equal, i.e., $\frac{\partial^2 ...
Partial DerivativesMultivariable CalculusMixed Partial Derivatives
2025/4/27
The problem asks for the first partial derivatives of several functions with two variables. We will ...
Partial DerivativesMultivariable CalculusDifferentiation
2025/4/27
We need to find the limit of the function $\frac{e^x + 2x - 1}{2e^x + 1}$ as $x$ approaches infinity...
LimitsL'Hopital's RuleExponential FunctionsCalculus
2025/4/26
We need to find the integral of the following expression: $\int \frac{dx}{\sin^3(x) \cos^5(x)}$
IntegrationTrigonometric FunctionsCalculus
2025/4/26
We are asked to evaluate the integral $\int \frac{dx}{\sin^3(x) \cos^5(x)}$.
CalculusIntegrationTrigonometric FunctionsDefinite IntegralsSubstitution
2025/4/26