Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
We are given two problems. Problem 12: Given $z = \arctan(xy)$ and two points $P(-2, -0.5)$ and $Q(-...
Partial DerivativesMultivariable CalculusTangent PlaneApproximationArctangent
2025/5/11
We are given the function $z = \ln(x^2y)$, and two points $P(-2, 4)$ and $Q(-1.98, 3.96)$. We need t...
Partial DerivativesTotal DifferentialMultivariable CalculusApproximation
2025/5/11
The problem asks to approximate the change in $z$ using the total differential $dz$ as $(x, y)$ move...
Partial DerivativesTotal DifferentialMultivariable CalculusApproximation
2025/5/11
Find the equation of the tangent plane to the surface $z = x^{1/2} + y^{1/2}$ at the point $(1, 4, 3...
Multivariable CalculusTangent PlanePartial DerivativesSurface
2025/5/11
The problem asks us to find the equation of the tangent plane to the given surface $z = 2e^{3y} \cos...
Multivariable CalculusTangent PlanePartial Derivatives
2025/5/11
The problem asks us to find the equation of the tangent plane to the surface $z = xe^{-2y}$ at the p...
Partial DerivativesTangent PlaneMultivariable Calculus
2025/5/11
We are asked to find the equation of the tangent plane to the given surfaces at the indicated points...
Multivariable CalculusTangent PlanePartial Derivatives
2025/5/11
We need to find the equation of the tangent plane to the surface $z = xe^{-2y}$ at the point $(1, 0,...
Multivariable CalculusTangent PlanePartial DerivativesGradients
2025/5/11
We are asked to find the equation of the tangent plane to the surface $z = 2e^{3y}\cos(2x)$ at the p...
Multivariable CalculusTangent PlanePartial DerivativesGradients
2025/5/11
We are given several math problems. We will solve problem IV, part b. It asks us to first show that...
IntegrationDefinite IntegralsSubstitutionCalculus
2025/5/11