Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
We are given the function $f(x) = \frac{x}{x^2 - 1}$. We need to: 1. Determine the domain $D_f$ of t...
Function AnalysisDomainOdd FunctionMonotonicityVariation Table
2025/5/6
The problem consists of three exercises. Exercise 1 involves finding the domain of functions, studyi...
Domain of FunctionsParity of FunctionsFunction EvaluationPreimages of FunctionsTrigonometric EquationsTrigonometric InequalitiesIntervalsVariations of Functions
2025/5/6
The problem asks to find the derivative of the function $y = \log |\log x|$. We assume that $\log$ d...
CalculusDifferentiationChain RuleLogarithms
2025/5/6
We are asked to find the values of constants $a$ and $b$ such that $\lim_{x \to 1} \frac{a\sqrt{x+1}...
LimitsCalculusL'Hopital's Rule (Implicit)RationalizationAlgebraic Manipulation
2025/5/6
We are asked to find the limit: $lim_{x \to 2} \frac{x^3 - 8}{\sqrt{x+2} - 2}$.
LimitsCalculusRationalizationIndeterminate Forms
2025/5/5
The problem asks to evaluate the limit of a constant function as $x$ approaches 2. The expression to...
LimitsConstant Function
2025/5/5
The problem asks us to find the area of the region $S$ bounded by the curve $y = \tan x$, the x-axis...
CalculusDefinite IntegralsAreaVolume of RevolutionTrigonometric FunctionsIntegration Techniques
2025/5/3
The problem asks us to find the equation of a tangent line $l$ drawn from the point $(0, 1)$ to the ...
CalculusTangent LinesIntegrationDefinite IntegralsLogarithmic Functions
2025/5/3
The problem asks us to find the equation of the tangent line $l$ to the curve $C: y = \log_2 x$ that...
CalculusTangent LinesLogarithmic FunctionsDefinite IntegralsArea Calculation
2025/5/3
The problem asks us to identify which of the given integral formulas resembles the integral $5 \int ...
IntegrationTrigonometric FunctionsSubstitutionIntegral Formulas
2025/5/2