Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
Find the directional derivative of the function $f(x, y, z) = x^2 + y^2 + z^2$ at the point $p = (1,...
Multivariable CalculusDirectional DerivativeGradientVector Calculus
2025/4/30
The problem asks us to find the directional derivative of the function $f(x, y, z) = x^3y - y^2z^2$ ...
Multivariable CalculusDirectional DerivativeGradient
2025/4/30
We are asked to find the gradient of the function $f(x, y, z) = xz \ln(x + y + z)$. The gradient is ...
Multivariable CalculusGradientPartial DerivativesLogarithmic Functions
2025/4/30
We are asked to find the gradient $\nabla f$ of the function $f(x, y, z) = x^2y + y^2z + z^2x$.
Multivariable CalculusGradientPartial DerivativesVector Calculus
2025/4/30
We need to find the limit of the function $f(x, y) = \frac{xy^2}{x^2 + y^4}$ as $(x, y)$ approaches ...
LimitsMultivariable CalculusPath DependenceFunctions of Several Variables
2025/4/30
The problem asks to find the limit of the function $\frac{\tan(x^2 + y^2)}{x^2 + y^2}$ as $(x, y)$ a...
LimitsMultivariable CalculusTrigonometric Functions
2025/4/30
We are asked to find the limit of the function $\frac{\tan(x^2 + y^2)}{x^2 + y^2}$ as $(x, y)$ appro...
LimitsMultivariable CalculusTrigonometric FunctionsL'Hopital's RuleSmall Angle Approximation
2025/4/30
The problem presents three parts, A, B, and C, involving functions $g(x)$, $h(x)$, $j(x)$, $k(x)$, a...
LogarithmsTrigonometryEquationsFunctionsExponential Functions
2025/4/30
The problem concerns the analysis of the function $f(x) = x^2 - x + \dots$. We are asked to: 1. Calc...
FunctionsDerivativesMonotonicityTangent LinesCalculus
2025/4/30
The problem consists of several parts related to the function $f(x) = x^2 - x + a$, where 'a' is a c...
FunctionsDerivativesMonotonicityTangentsQuadratic FunctionsCalculus
2025/4/30