Calculus 1, the mathematical wizardry behind change and motion, holds immense power in unraveling the secrets of our world. Whether you’re a high school student embarking on a mathematical adventure or a university student delving deeper into its mysteries, this article will be your
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The p-Series test provides a criterion for determining the convergence of a particular type of series known as the p-Series. A p-Series is defined as a series of the form $\sum_{n=1}^\infty \frac{1}{n^p}$, where p is a positive constant. When studying series in mathematics, determining whether a series converges or diverges is of utmost importance. The
Exploring the root Test and determining series convergence through limiting roots. In
Geometric series are a fundamental concept in mathematics, frequently encountered in various
We propose a nice proof of Peano existence theorem. This theorem shows that the continuity of the vector field suffices for the
In this post, we study Fourier transform properties and give some applications. In fact, this transformation helps in converting partial differential equations
We offer a selection of improper integral exercises with detailed answers. Our main objective is to show you how to prove that
We propose exercises on functions defined by integrals. We mainly prove the regularity of such a function, like continuity and differentiability. These
We propose simple techniques to learn you how to find the limit of a function. We first recall what a limit of
We offer practical tips for learning basic to advanced math. Above all, mathematics is a difficult and abstract subject, while a part
Parameter-dependent integral is studied in this article. We propose a selection of exercises on continuity, limit, and differentiability of such parametric integrals.
In this article, we offer exercises on convex functions. In fact, our objectives are: to be able to show that a function
Recurring sequences are generally involved in the modeling of discrete systems. In fact, such sequences replace the differential equation by discretizing the
We discuss the convergence of sequences and how to calculate the limit of a sequence. This subject is fundamental in real analysis
We offer exercises on differential calculus with detailed answers. In fact, our objectives are as follows: knowing how to calculate the derivative
The maximal solution to Cauchy’s problems is a solution that gives full information on the physical model. In fact, we obtain this