Analysis

Problems related to calculus, limits, series, etc.

Problems in this category

We are asked to change the given integral to polar coordinates and then evaluate it. The given integ...

Multiple IntegralsChange of VariablesPolar CoordinatesIntegration Techniques

We are asked to evaluate the triple integral $\int_{0}^{\log 2} \int_{0}^{x} \int_{0}^{x+y} e^{x+y+z...

Multiple IntegralsTriple IntegralIntegration

We need to find the limit of the given expression as $x$ approaches infinity: $\lim_{x \to \infty} \...

LimitsCalculusAsymptotic Analysis

We are asked to find the limit of the expression $\frac{2x - \sqrt{2x^2 - 1}}{4x - 3\sqrt{x^2 + 2}}$...

LimitsCalculusRationalizationAlgebraic Manipulation

We are asked to find the limit of the given expression as $x$ approaches infinity: $\lim_{x\to\infty...

LimitsCalculusSequences and SeriesRational Functions

The problem asks us to find the limit as $x$ approaches infinity of the expression $\frac{2x - \sqrt...

LimitsCalculusAlgebraic ManipulationRationalizationSequences and Series

We are asked to evaluate the following limit: $\lim_{x \to 1} \frac{x^3 - 2x + 1}{x^2 + 4x - 5}$.

LimitsCalculusPolynomial FactorizationIndeterminate Forms

We need to find the limit of the expression $\frac{2x^3 - 2x + 1}{x^2 + 4x - 5}$ as $x$ approaches $...

LimitsCalculusRational FunctionsPolynomial DivisionOne-sided Limits

The problem is to solve the equation $\sin(x - \frac{\pi}{2}) = -\frac{\sqrt{2}}{2}$ for $x$.

TrigonometryTrigonometric EquationsSine FunctionPeriodicity

We are asked to evaluate the limit: $\lim_{x \to +\infty} \frac{(2x-1)^3(x+2)^5}{x^8-1}$

LimitsCalculusAsymptotic Analysis

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