Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
We are asked to find the limit of the function $\frac{(2x-1)^3(x+2)^5}{x^8-1}$ as $x$ approaches inf...
LimitsFunctionsAsymptotic Analysis
2025/5/29
We need to evaluate the definite integral and subtract a constant. The expression is: $A(R) = \int_{...
Definite IntegralIntegrationCalculus
2025/5/28
We are asked to evaluate the definite integral $\int_{-4}^3 [3-x-(x^2-a)] dx - \frac{\pi 3^2}{2}$.
Definite IntegralIntegrationCalculus
2025/5/28
We are asked to find the area bounded by the function $f(x) = \frac{4}{3}x^3 - 7.5x^2 + 10x$, the x-...
CalculusDefinite IntegralFinding MaximaDerivativesArea under a curve
2025/5/28
We need to find the area of the region limited by the graphs of the following functions: a) $f(x) = ...
Definite IntegralsArea CalculationAbsolute ValuePiecewise FunctionsCalculus
2025/5/28
The problem asks to find the area of the region bounded by the graph of $f(x) = |x| - |x-1|$ on the ...
Absolute ValueIntegrationPiecewise FunctionsDefinite IntegralArea Calculation
2025/5/28
We need to find the convergence set for the given power series. Let's solve the problems one by one.
Power SeriesRatio TestInterval of ConvergenceSeries Convergence
2025/5/28
We need to determine the convergence or divergence of the series $\sum_{n=1}^{\infty} \frac{n^3}{(2n...
SeriesConvergenceDivergenceRatio TestLimits
2025/5/28
Determine the convergence or divergence of the series $\sum_{n=1}^{\infty} \frac{n^3}{(2n)!}$ using ...
SeriesConvergenceDivergenceRatio TestLimits
2025/5/28
We are asked to show that the series $\sum_{n=1}^{\infty} (-1)^{n+1} \frac{1}{n(n+1)}$ and $\sum_{n=...
SeriesConvergenceAbsolute ConvergenceLimit Comparison TestRatio Test
2025/5/28