Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
The problem has two parts. a) We are given two statements about functions and intervals, and we need...
CalculusLocal ExtremaGlobal ExtremaRolle's TheoremHyperbolic Functions
2025/4/28
We are given the function $f(x, y) = \frac{x^2}{y}$ and the point $p = (2, -1)$. We need to find the...
Multivariable CalculusPartial DerivativesGradient VectorTangent Plane
2025/4/28
The problem asks us to find the gradient vector of a given function $f(x, y)$ at a given point $p$, ...
Multivariable CalculusPartial DerivativesGradient VectorTangent Plane
2025/4/28
We are asked to find the gradient vector and the equation of the tangent plane of a given function $...
Multivariable CalculusPartial DerivativesGradient VectorTangent Plane
2025/4/28
We want to show that the limit $\lim_{(x,y)\to(0,0)} \frac{xy}{x^2+y^2}$ does not exist. We will do...
LimitsMultivariable CalculusPathwise LimitsContinuity
2025/4/28
The problem asks us to prove that the limit of the sum of two functions $f(x, y)$ and $g(x, y)$ as $...
LimitsMultivariable CalculusLimit PropertiesProof
2025/4/28
We are given a function $f(x, y)$ defined piecewise as follows: $f(x, y) = \begin{cases} \frac{x^2 -...
LimitsContinuityMultivariable Calculus
2025/4/28
The problem asks to determine the largest set S on which the given functions f are continuous. We ne...
ContinuityMultivariable CalculusDomainFunctions of Several Variables
2025/4/28
The problem asks us to find the antiderivatives (indefinite integrals) of a set of given functions. ...
IntegrationAntiderivativesCalculusPower RuleIndefinite Integrals
2025/4/28
The problem asks us to find the antiderivatives of a list of functions. In other words, we need to f...
IntegrationAntiderivativesPower Rule
2025/4/28