Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
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
We are asked to find the derivative of the function $f(x) = (x+2)^x$ using logarithmic differentiati...
DifferentiationLogarithmic DifferentiationChain RuleProduct RuleDerivatives
2025/4/1
We need to evaluate the integral $\int \frac{e^x}{e^{3x}-8} dx$.
IntegrationCalculusPartial FractionsTrigonometric Substitution
2025/4/1
We are asked to evaluate the integral: $\int \frac{e^{2x}}{e^{3x}-8} dx$
IntegrationCalculusSubstitutionPartial FractionsTrigonometric Substitution
2025/4/1