Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
We are asked to compute three limits: A. $\lim_{x \to 2} \frac{x^3 - 8}{\sqrt{x+2} - 2}$ B. $\lim_{x...
LimitsCalculusL'Hopital's RuleTrigonometric Functions
2025/5/11
We need to find the correct solution for the integral $\int x^2 \sin x \, dx$.
IntegrationIntegration by PartsDefinite Integral
2025/5/10
Given the function $f(x) = e^x + (5)^x$, we need to find the value of its derivative at $x=0$, i.e.,...
CalculusDerivativesExponential Functions
2025/5/10
The problem asks us to identify which of the given improper integrals converges. A. $\int_{1}^{\inft...
CalculusIntegrationImproper IntegralsConvergenceDivergence
2025/5/10
The problem asks to find the derivative of the function $f(x) = \text{sech}^{-1}(2x)$ at $x = 0.1$.
CalculusDerivativesInverse Hyperbolic FunctionsDifferentiation
2025/5/10
The problem asks us to find the correct trigonometric substitution to evaluate the integral $\int \s...
IntegrationTrigonometric SubstitutionDefinite IntegralsCalculus
2025/5/10
We need to find the area of the shaded region enclosed by the curves $y = 2x^2 + 2$ and $y = 2x + 6$...
Area between curvesDefinite integralQuadratic equations
2025/5/10
The problem asks us to evaluate the definite integral $\int_1^2 (\frac{1}{x^2} - \frac{1}{x^3}) \, d...
Definite IntegralsIntegrationProperties of Integrals
2025/5/10
We are given that $f(x) \ge 0$ for $a \le x \le b$, and that $\int_a^b f(x) \, dx \ge (k+4+3)$. We w...
Definite IntegralsInequalitiesCalculus
2025/5/10
The problem asks us to find the overestimate of the area under the curve $f(x) = x^3$ on the interva...
CalculusDefinite IntegralsRiemann SumsApproximation
2025/5/10