Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
We are given the function $f(x) = x^2 + 1$ and we want to determine the interval(s) in which its rec...
CalculusDerivativesFunction AnalysisIncreasing Functions
2025/4/5
We are given the function $f(x) = -2x + 3$. We want to find where the reciprocal function, $g(x) = \...
CalculusDerivativesIncreasing FunctionsReciprocal FunctionsAsymptotes
2025/4/5
We need to find the horizontal asymptote of the function $f(x) = \frac{2x - 7}{5x + 3}$.
LimitsAsymptotesRational Functions
2025/4/5
Given the function $f(x) = \frac{x^2+3}{x+1}$, we need to: 1. Determine the domain of definition of ...
FunctionsLimitsDerivativesDomain and RangeAsymptotesFunction Analysis
2025/4/3
We need to evaluate the limit: $\lim_{x \to +\infty} \ln\left(\frac{(2x+1)^2}{2x^2+3x}\right)$.
LimitsLogarithmsAsymptotic Analysis
2025/4/1
We are asked to solve the integral $\int \frac{1}{\sqrt{100-8x^2}} dx$.
IntegrationDefinite IntegralsSubstitutionTrigonometric Functions
2025/4/1
We are given the function $f(x) = \cosh(6x - 7)$ and asked to find $f'(0)$.
DifferentiationHyperbolic FunctionsChain Rule
2025/4/1
We are asked to evaluate the indefinite integral $\int -\frac{dx}{2x\sqrt{1-4x^2}}$. We need to find...
IntegrationIndefinite IntegralSubstitutionInverse Hyperbolic Functionssech⁻¹
2025/4/1
The problem asks us to evaluate the integral $\int -\frac{dx}{2x\sqrt{1-4x^2}}$.
IntegrationDefinite IntegralSubstitutionTrigonometric Substitution
2025/4/1
We are asked to evaluate the definite integral $\int_{\frac{7}{2\sqrt{3}}}^{\frac{7\sqrt{3}}{2}} \fr...
Definite IntegralIntegrationTrigonometric SubstitutionInverse Trigonometric Functions
2025/4/1