Analysis

Problems related to calculus, limits, series, etc.

Problems in this category

The problem asks us to graph the function $f(x) = 2 \cdot (\frac{1}{2})^x$ on the provided coordinat...

Exponential FunctionsGraphingFunction Analysis

The problem is to analyze the exponential function $f(x) = 3 \cdot 2^x$. The image shows the graph c...

Exponential FunctionsFunction AnalysisGraphing

We are asked to evaluate the summation of the expression $n-1$ from $n=c_1$ to $\xi$. It is likely t...

SeriesSummationDivergenceInfinite Series

The problem is divided into two exercises. Exercise 3 is about the function $f(x) = \frac{x}{x^2 - 1...

FunctionsDomainOdd FunctionsDerivativesTrigonometryTrigonometric EquationsTrigonometric InequalitiesIntervalsVariation

The problem states that if $f$ is a continuous function that satisfies $\int_0^x f(t) dt = x^2(1+x)$...

CalculusFundamental Theorem of CalculusIntegrationDifferentiationDefinite Integral

We need to evaluate the definite integral $I = \int_{-1}^{1} \frac{x}{1 + |x|} \, dx$.

Definite IntegralIntegrationAbsolute ValueCalculus

We need to evaluate the definite integral $J = \int_{0}^{1} x^4 (1 - x^2)^{3/2} dx$.

Definite IntegralTrigonometric SubstitutionIntegration TechniquesReduction Formula

We need to evaluate the limit of the function $\log_2(\frac{1}{x})$ as $x$ approaches 0 from the pos...

LimitsLogarithmsFunction Analysis

We want to find the limit of $2^{-x}$ as $x$ approaches infinity. In other words, we need to find $...

LimitsExponential FunctionsCalculus

The problem asks to evaluate the limit: $ \lim_{x \to 3^+} \frac{x^2 - 3x}{|x-3|} $

LimitsFunctionsAbsolute ValueCalculus

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