Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
Solve the inequality $\sin(\theta + \frac{\pi}{6}) < \frac{1}{\sqrt{2}}$ for $0 \le \theta < 2\pi$.
TrigonometryInequalitiesTrigonometric Functions
2025/5/9
The problem asks us to find the partial derivative of $z$ with respect to $t$, denoted as $\frac{\pa...
Partial DerivativesChain RuleMultivariable Calculus
2025/5/9
The problem asks us to find $\frac{\partial w}{\partial \theta}$ for $w = x^2y + z^2$, where $x = \r...
Partial DerivativesChain RuleMultivariable Calculus
2025/5/9
We need to find $\frac{dw}{dt}$ for each of the given functions using the chain rule, and express th...
Chain RulePartial DerivativesMultivariable Calculus
2025/5/9
The problem has three parts: (a) Given the set $A = [-7, 8) \cup [11, \infty)$, find the complement ...
Set TheoryCalculusIntegration by PartsDefinite Integral
2025/5/8
The problem asks to evaluate the definite integral $2\pi \int_{0}^{50} (12 + \frac{\sqrt{y^3(50-y)}}...
Definite IntegralSurface Area of RevolutionCalculusIntegration
2025/5/8
The problem consists of three parts: (i) Evaluate the definite integral $\int_{2}^{3} (t^2 - 3) dt$....
Definite IntegralsLinear FunctionsRepeating DecimalsFunctions
2025/5/8
The problem consists of three parts: (i) Differentiate $y = 2x^3 \sin(2x)$. (ii) Simplify $(\frac{8}...
DifferentiationExponentsRadicalsRationalizationProduct Rule
2025/5/8
The problem asks us to find the derivative of the function $y = -x^3(3x^4 - 2)$.
DifferentiationPower RuleDerivativesCalculus
2025/5/8
Given that $f$ is a continuous function and that $\int_0^{x^2(1+x)} f(t) dt = x$, we need to calcula...
CalculusDefinite IntegralsFundamental Theorem of CalculusChain RuleDifferentiation
2025/5/7