Analysis

Problems related to calculus, limits, series, etc.

Problems in this category

We need to determine if the function $f(x) = \sin(x)$ is even, odd, or neither.

TrigonometryFunction PropertiesEven FunctionsOdd FunctionsSine Function

Find the first and second derivatives of the function $y = \frac{1+3x}{3x}(3-x)$.

DerivativesDifferentiationCalculusFunctions

The problem asks to find the first and second derivatives of the function $y = \frac{x^4}{2} - \frac...

DifferentiationDerivativesPower Rule

We are asked to find the sum of the areas of the three regions enclosed by the parabola $y = x^2 - 2...

CalculusIntegrationDefinite IntegralsArea CalculationParabola

The problem asks us to find the function $f(x)$ and the constant $a$ that satisfy the equation $\int...

CalculusDefinite IntegralsFundamental Theorem of CalculusFunctions

The problem asks to find the area $S$ enclosed by the parabola $y = -x^2 - 4x$ and the x-axis. Also...

Definite IntegralsArea CalculationParabolaIntersection Points

We are asked to find the area S enclosed by the given parabolas and the x-axis. (1) $y = -x^2 - 4x$ ...

CalculusIntegrationDefinite IntegralsArea CalculationParabolas

We are asked to evaluate the definite integral of the function $y = x^2 + 4x + 3$. The integral is g...

Definite IntegralAntiderivativeCalculus

The problem is to evaluate the definite integrals $\int_{1}^{2} (4x^2+3x-1)dx - \int_{1}^{3} (4x^2+3...

Definite IntegralsIntegrationPolynomialsCalculus

The problem asks us to evaluate the sum of two definite integrals: $\int_{-2}^{1} (x^2+2x+7) dx + \i...

Definite IntegralsIntegrationFundamental Theorem of Calculus

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