Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
a) We are given the function $f(x) = \sqrt{ax - b}$, where $a, b \in \mathbb{R}$ and $a > 0$. We nee...
LimitsInverse Hyperbolic FunctionsCalculus
2025/4/11
We are asked to evaluate the limit of a vector-valued function as $t$ approaches 0. The vector-value...
LimitsVector CalculusMultivariable CalculusLimits of Vector-Valued Functions
2025/4/11
We are given a function $f(x)$ defined as a determinant: $f(x) = \begin{vmatrix} \sin x & \cos x & \...
DeterminantsDerivativesTrigonometryCalculus
2025/4/10
The problem consists of several exercises. Exercise 5 asks us to consider two functions, $f(x) = 2\c...
TrigonometryTrigonometric IdentitiesFunctions
2025/4/10
We are asked to evaluate the following integral: $\int_0^{+\infty} \frac{dx}{(1+x)(\pi^2 + \ln^2 x)}...
Definite IntegralIntegration TechniquesSubstitutionCalculus
2025/4/7
We need to find the average rate of change of the function $f(x) = \frac{x-5}{x+3}$ from $x = -2$ to...
Average Rate of ChangeFunctionsCalculus
2025/4/5
If a function $f(x)$ has a maximum at the point $(2, 4)$, what does the reciprocal of $f(x)$, which ...
CalculusFunction AnalysisMaxima and MinimaReciprocal Function
2025/4/5
We are given the function $f(x) = x^2 + 1$ and we want to determine the interval(s) in which its rec...
CalculusDerivativesFunction AnalysisIncreasing Functions
2025/4/5
We are given the function $f(x) = -2x + 3$. We want to find where the reciprocal function, $g(x) = \...
CalculusDerivativesIncreasing FunctionsReciprocal FunctionsAsymptotes
2025/4/5
We need to find the horizontal asymptote of the function $f(x) = \frac{2x - 7}{5x + 3}$.
LimitsAsymptotesRational Functions
2025/4/5