Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
The problem asks to evaluate the limit of the expression $x^2 + xe^x$ as $x$ approaches $0$. That is...
LimitsCalculusExponential FunctionsContinuity
2025/4/29
We are given a first-order differential equation and we are asked to solve it. The equation is $y' =...
Differential EquationsFirst-order Differential EquationHomogeneous Differential EquationSeparation of Variables
2025/4/29
The problem asks to solve the differential equation: $y' = \frac{x-y}{x+y}$
Differential EquationsHomogeneous EquationsIntegrationSubstitution
2025/4/29
We are given the limit $ \lim_{x \to \infty} (\sqrt[3]{x^3 + ax^2} - \sqrt[3]{bx^3 - 5x^2 + 1}) = 2 ...
LimitsCalculusBinomial ApproximationCube RootsAlgebra
2025/4/29
We need to evaluate the integral: $I = \int \frac{x^2}{\sqrt{1-x^2}} dx$
IntegrationTrigonometric SubstitutionDefinite IntegralsCalculus
2025/4/28
We are asked to evaluate the integral $J = \int \frac{dx}{(x^2 + 1)^2}$.
IntegrationTrigonometric SubstitutionDefinite IntegralsCalculus
2025/4/28
We are asked to find the limit of a vector-valued function as $t$ approaches infinity. The vector-va...
LimitsVector-Valued FunctionsCalculus
2025/4/28
We are asked to find the derivative of the function $y = \frac{e^{3x}}{(x^2+3)^2(1+\cos x)^4}$ using...
DifferentiationLogarithmic DifferentiationCalculusChain Rule
2025/4/28
The problem involves analyzing the function $f(x) = \ln|x^2 - 1|$. We need to find the domain, inter...
CalculusFunctionsDomainLimitsDerivativesCritical PointsConcavityGraphing
2025/4/28
The first problem asks to find the value of $a$ such that the function $f(x)$ is continuous at $x=1$...
LimitsContinuityFunctionsAlgebraic Manipulation
2025/4/28