Analysis

Problems related to calculus, limits, series, etc.

Problems in this category

We are asked to find a formula for each of the given summations: a) $\sum_{i=1}^{n} (\sqrt{2i+1} - \...

SummationSeriesTelescoping SumGeometric SeriesLogarithmsPartial Fractions

We need to evaluate the definite integral: $\int_{-1}^{0} \frac{dx}{4x^2 + 8x + 8}$

Definite IntegralIntegrationSubstitutionCompleting the SquareTrigonometric Functions

We need to evaluate the definite integral: $\int_{-1}^{\infty} \frac{dx}{4x^2+8x+8}$.

Definite IntegralIntegrationCompleting the SquareSubstitutionTrigonometric Functions

The problem is about the function $y = x^3 - x$ and its graph $C$. a) Show that $A(-1, 0)$ is an int...

CalculusFunctionsTangentsIntersection of curvesDerivativesQuadratic Equations

We need to find the indefinite integral of the function $\frac{x+4}{x^2+4}$.

IntegrationIndefinite IntegralSubstitutionTrigonometric SubstitutionCalculus

We need to evaluate the definite integral $J = \int \frac{x^2+x-2}{x^4+5x^2+4} dx$.

Definite IntegralPartial Fraction DecompositionIntegrationCalculus

We are asked to solve the Cauchy problem for the differential equation $y'' - 3y' = 0$ with initial ...

Differential EquationsCauchy ProblemSecond-order Linear Differential EquationInitial Value ProblemCharacteristic EquationHomogeneous Equation

Evaluate the double integral $\iint_S x \, dA$, where $S$ is the region between the curves $y = x$ a...

Double IntegralsRegion of IntegrationCalculusIntegration

We need to evaluate the double integral $\iint_S \frac{2}{1+x^2} dA$, where $S$ is the triangular re...

Double IntegralsMultivariable CalculusIntegrationAreaTrigonometric FunctionsLogarithmic Functions

We are asked to evaluate six iterated integrals.

Iterated IntegralsDouble IntegralsCalculus

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