Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
The problem asks to graph the function $y = \cos(\frac{\pi}{6}x)$.
TrigonometryCosine FunctionGraphingPeriodAmplitudePhase Shift
2025/3/16
The problem asks to graph the function $y = \cos(x - \frac{\pi}{6})$.
TrigonometryCosine FunctionGraphingPhase ShiftAmplitudePeriod
2025/3/16
Find the equation of the tangent line $g$ to the graph of the function $y = \tan x$ at the point $(\...
CalculusDifferentiationTangent LinesTrigonometry
2025/3/16
The problem asks to find the equation of the tangent line $g$ to the graph of the function $y = \tan...
CalculusDerivativesTangent LinesTrigonometry
2025/3/16
The problem states that the line $g$ is tangent to the graph of the function $y = \tan x$ at the poi...
CalculusDerivativesTangent LinesTrigonometryDifferentiation
2025/3/16
We need to find the limit of the expression $\frac{n^2}{(n+1)^2}$ as $n$ approaches infinity.
LimitsSequencesCalculus
2025/3/15
We are asked to find the limit of the given expression as $n$ approaches infinity: $$ \lim_{n \to \i...
LimitsSequencesCalculusAsymptotic Analysis
2025/3/15
The problem asks us to find the value of the infinite sum $\sum_{n=1}^{\infty} \frac{x^n}{n^2}$.
Infinite SeriesPolylogarithm FunctionDilogarithmConvergenceSpecial Values
2025/3/15
The problem asks us to evaluate the infinite sum $\sum_{n=1}^{\infty} \frac{x^n}{(n-1)!}$.
Infinite SeriesTaylor SeriesExponential FunctionSummation
2025/3/15
We are asked to solve a series of calculus problems including finding roots of equations, finding ra...
TrigonometryTrigonometric EquationsFunctionsEven and Odd FunctionsCalculusDerivativesDomain and Range
2025/3/14