Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
The image contains several mathematics problems. We will solve problem number 8 which asks us to fin...
IntegrationPartial FractionsCalculusDefinite Integral
2025/5/18
The problem asks to prove the formula for the Fourier coefficient $b_n$ given the Fourier series exp...
Fourier SeriesOrthogonalityIntegration
2025/5/18
The problem states that a function $f(x)$ is defined on an open interval $(-L, L)$ and has period $2...
Fourier SeriesOrthogonalityIntegration
2025/5/18
The problem states that given the function $g(x) = \frac{xe^x}{e^x + 1}$, we need to show that $g(a)...
FunctionsExponentialsRoots of EquationsInequalities
2025/5/18
We are given the limit of a rational function as $x$ approaches infinity: $\lim_{x\to\infty} \frac{8...
LimitsRational FunctionsCalculus
2025/5/18
We are given the limit of a rational function as $x$ approaches infinity: $$ \lim_{x \to \infty} \fr...
LimitsRational FunctionsAsymptotes
2025/5/18
The problem is to solve the second-order non-homogeneous linear differential equation: $2y'' + y' - ...
Differential EquationsLinear Differential EquationsSecond-Order Differential EquationsNon-homogeneousHomogeneous SolutionParticular Solution
2025/5/17
The text contains statements about the relationship between injective (one-to-one) and surjective (o...
FunctionsInjectiveSurjectiveOne-to-oneOntoMappingSet Theory
2025/5/17
The problem is to determine whether the function $F(x) = \sin(x) - x + x^2$ is even, odd, or neither...
Function PropertiesEven and Odd FunctionsTrigonometric Functions
2025/5/17
The problem asks us to determine if the function $f(x) = \cos(x)$ is even or odd. We need to evaluat...
FunctionsEven and Odd FunctionsTrigonometryCosine Function
2025/5/17