Analysis

Problems related to calculus, limits, series, etc.

Problems in this category

We are given a sequence $(u_n)$ defined by $u_0 = 9e$ and $u_{n+1} = 3\sqrt{u_n}$ for all $n \in \ma...

SequencesLogarithmsGeometric SequencesRecursive Sequences

We are given a sequence $(u_n)$ defined by $u_0 = 1$ and $u_{n+1} = \frac{2u_n}{u_n+2}$ for all $n \...

SequencesSeriesConvergenceArithmetic SequencesLimits

We are asked to solve the integral $\int \frac{e^x}{4(1+e^{2x})} dx$.

IntegrationSubstitutionCalculus

We need to evaluate the definite integral $\int_{0}^{\sqrt{3}} \frac{dx}{4x^2+1}$.

Definite IntegralTrigonometric SubstitutionAntiderivativesArctangent

The problem consists of four questions related to Calculus. 1. a) Determine all the roots of three ...

CalculusDerivativesInverse FunctionsTrigonometric IdentitiesDomain and RangeTrigonometric Equations

The problem requires us to find the arc length of the curve defined by the parametric equations $x =...

Arc LengthParametric EquationsCalculusIntegration

We are asked to evaluate the definite integral $\int_0^1 x(1+x)^{2022} dx$.

Definite IntegralIntegration by SubstitutionPower Rule

We are given the function $g(x) = x^2 - 1 + \ln x$ defined on the interval $]0, +\infty[$. We need t...

CalculusDerivativesFunction AnalysisMonotonicityLogarithmic Functions

The problem asks us to evaluate the integral $\int \frac{1}{\sin x - \cos x} dx$.

IntegrationTrigonometric FunctionsSubstitutionCalculus

Find the value of $\alpha$ given that $\sin{\alpha} = 1$.

TrigonometrySine FunctionSolving EquationsRadians

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