Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
We are asked to evaluate the integral $\int \frac{2x+1}{(x-1)(x^2+1)} dx$.
IntegrationPartial FractionsCalculus
2025/5/2
The question asks which of the following integrals is easily integrated by substituting $x = 6 \tan ...
IntegrationTrigonometric SubstitutionDefinite Integrals
2025/5/2
The problem asks which of the given integrals requires integration by parts only once. The options a...
IntegrationIntegration by PartsDefinite Integrals
2025/5/2
The problem asks which integral resembles $\int x^2 \sqrt{x^2 - 9} \, dx$. We need to identify the c...
IntegrationSubstitutionDefinite IntegralsCalculus
2025/5/2
The problem asks to find the right-hand limit of the function $f(x) = \text{Int}(x)$ as $x$ approach...
LimitsFloor FunctionReal Analysis
2025/5/2
We are given a function $f(x) = \frac{11x - 5}{5}$ and asked to find the value of $f'(1.2)$.
DifferentiationDerivativesFunctions
2025/5/2
We are asked to find the limit of the function $x^2 + xe^x$ as $x$ approaches infinity. That is, we ...
LimitsCalculusInfinityExponential Functions
2025/5/2
The problem asks to evaluate the limit $\lim_{x \to 0} \frac{(1-\cos x)^2}{\tan^3 x - \sin^3 x}$.
LimitsTrigonometryTaylor SeriesL'Hopital's Rule
2025/5/1
The problem asks us to find the period of the function $y = 10 \sin(\frac{6\pi}{4}(x - \frac{\pi}{2}...
TrigonometryPeriodic FunctionsSine FunctionPeriod
2025/5/1
The problem asks to find the value of $k$ in the equation $15\sin(kt)$ such that the period of the f...
TrigonometryPeriodic FunctionsSine FunctionPeriod
2025/5/1