Analysis

Problems related to calculus, limits, series, etc.

Problems in this category

The problem asks to find the mass $m$ and the center of mass $(\bar{x}, \bar{y})$ of a lamina bounde...

Multivariable CalculusDouble IntegralsCenter of MassLaminaDensity Function

The problem asks us to find the value(s) of $a$ such that the function $f(x) = x^3 + ax^2 + 3x - 4$ ...

CalculusDerivativesIncreasing FunctionQuadratic InequalitiesDiscriminant

The problem is to evaluate the double integral $\int_0^{\pi/2} [\frac{1}{2} \int_4^0 \sqrt{u} \, du ...

CalculusIntegrationDouble IntegralDefinite Integral

We need to evaluate the double integral $\iint_S y \, dA$, where $S$ is the region in the first quad...

Double IntegralsPolar CoordinatesMultivariable Calculus

We need to evaluate the double integral $\iint_S \sqrt{4-x^2-y^2} \, dA$, where $S$ is the first qua...

Multiple IntegralsDouble IntegralsPolar CoordinatesIntegrationCalculus

The problem asks to reverse the order of integration of the iterated integral $\int_0^1 \int_{-y}^y ...

Iterated IntegralsChange of Order of IntegrationCalculus of Several Variables

We are given the iterated integral $\int_{0}^{1} \int_{x^2}^{x^{1/4}} f(x, y) dy dx$. We need to cha...

Iterated IntegralsChange of Integration OrderCalculus

We are given the iterated integral $\int_{-\pi/2}^{\pi/2} \int_{0}^{\theta} kr dr d\theta$. The goal...

Iterated IntegralsDouble IntegralsCenter of MassPolar CoordinatesCalculus

We are asked to analyze the iterated integral $\int_0^2 \int_0^x k \, dy \, dx$. The goal is to sket...

Double IntegralsCenter of MassDensityIterated IntegralsCalculusMultivariable Calculus

The problem asks to calculate the area under the curve of the given functions between the specified ...

CalculusIntegrationDefinite IntegralArea under a curve

前へ 1...6 7 8 9 10...55 次へ