The user wants an aesthetic LaTeX template in Spanish for math analysis exercise solutions. I'll build a complete compilable document with custom theorem boxes via tcolorbox, nice fonts, headers/footers, a title page, and example exercises like limits, continuity, derivatives, sequences, and series to showcase the design. I'm deciding on the font and color scheme, planning to use newpxtext/newpxmath for an elegant Palatino-style look with a coordinated color palette, then layering in tcolorbox for exercise and solution boxes, amsthm for theorem environments, and fancyhdr for polished headers and footers. I'm also mapping out custom environments for exercises and solutions with QED markers, shorthand math commands like \R and \norm{}, Spanish language support via babel, TikZ/pgfplots for figures, and a clean title block with table of contents, then sketching a sample exercise in Spanish involving an epsilon-delta limit proof. Now I'm planning more exercises covering sequence convergence, continuity with a sin(1/x) plot, telescoping series, the mean value theorem, and an improper integral, plus styled theorem, definition, and observation boxes. For the boxes, I'm designing exercise boxes with a colored left bar and title, solution boxes that are breakable with a "Solución" heading ending in ∎, and theorem boxes with a colored title bar — making sure everything compiles cleanly under pdfLaTeX with Spanish babel settings to handle typography correctly. Writing the document preamble... I'm deciding to skip paragraph indentation and use spacing instead for a cleaner exercise-sheet look, then moving on to defining a color palette for the document with primary blue, light blue, and green tones. Setting up colors and the tcolorbox package... Still writing ejercicio box styling... Adding the closing square symbol... Now I'm setting up a themed theorem-box style using `\newtcbtheorem` for "Teorema" boxes, with a light red background, red frame border, bold title, and the title attached to the top left corner. I'm deciding to use `\newtcbtheorem` for teorema, definición, proposición, and lema environments (with optional empty number/label args), while keeping simpler `\newtcolorbox` definitions for observación and nota. Actually, I'm reconsidering a simpler approach combining amsthm with `\tcolorboxenvironment`, defining the theorem counter and styling, then customizing the heading color via `\newtheoremstyle` since the plain amsthm look is too plain. Writing theorem style config... Finishing the head spec with name, number, and a colored note in normal weight, then reconsidering whether to just use tcolorbox's built-in theorem environment via `\newtcbtheorem` instead, since it pairs more cleanly with `\tcolorboxenvironment` for styling. Setting both to 0pt should be safe since amsthm just uses those values for preskip/postskip in its trivlist setup, letting tcolorbox fully control the spacing instead. Now I'm configuring the tcolorboxenvironment hook for the teorema environment to handle the "before upper" styling. For exercises, I'm defining an auto-numbered tcolorbox with a title like "Ejercicio N" plus an optional subtitle argument, and considering how to support labeling via tcolorbox's label key so exercises can be cross-referenced. I should double check that etoolbox is actually available since tcolorbox depends on it, but I'll load it explicitly to be safe. I also want to confirm `\ifblank` works correctly when used inside the title since it's typeset later rather than expanded immediately, which should be fine given how tcolorbox handles title macros. Now I'm designing the exercise box itself, using auto counter numbered within section, with a dark blue title bar, white title text, and light blue background for the body... Setting `number within=section` so exercises display as "section.number" feels right for a structured sheet with topics like sequences, limits, derivatives, and integrals—letting exercises read as 1.1, 1.2, etc. I'm deciding against fancy shadows for the exercise box to keep things print-friendly and clean, skipping drop shadows entirely since they can look odd across page breaks. Now I'm defining the solution box style... Adding more box config... One concern I'm noting: ending the solution with a right-aligned square mark works fine for regular text, but could be awkward if the solution ends in a math display environment. Now I'm designing a separate "Observación" box with a gray color scheme and smaller font, giving it its own colored border and header styling. Next I'm setting up theorem-style environments for Theorem, Definition, Proposition, and Lemma using amsthm combined with tcolorbox, defining custom theorem styles with sans-serif bold headers. I'm working through how to color only the heading text rather than the entire body, since coltext applies globally—I need a per-environment approach that colors just the theorem head. Actually, defining a macro that gets set before the head is overcomplicated. It's simpler to just define separate theorem styles per color, each with its own colored head font. I'm adjusting the note formatting so the color and font apply correctly within the theorem head group, making sure the font change inside `\thmnote` stays scoped properly since it's the last element in the head spec. I recall now: `\thm@notefont` defaults to upright medium weight, and when the ninth argument to `\newtheoremstyle` is left empty, it falls back to using `\thmhead@plain`, which is the routine that assembles name, number, and note in the standard order. So the note still inherits the color from the head font since it's typeset within the same group, and the punctuation from `\thm@headpunct` gets appended within that same font context too. That confirms leaving the head spec empty gives me exactly the layout I want — bold colored name and number, medium-weight colored note, with the period styled consistently. Now for `tcolorboxenvironment{teorema}`, I'm setting up a box with a light red background, thin colored left rule, slightly rounded corners, and modest padding so it reads as a highlighted callout rather than a heavy frame. Thinking about visual hierarchy across the whole document, I'm settling on a consistent language: exercises get a full titled box with rounded corners and a dark header bar, solutions use a simple left green bar with no background, theory elements (theorems, definitions, propositions) use a light background with a sharp-cornered left colored bar, and notes get a smaller gray left-bar style. This keeps exercises as the primary visual focus while theory stays reference-like. I'm now moving into configuring section title formatting with titlesec. Adding fancyhdr config... I'm setting up hyperref with colored links and PDF metadata, plus considering cleveref for Spanish-language cross-reference names, and thinking about custom naming for the exercise box counters. I need makeatletter for that counter name. Since cleveref requires loading after hyperref, and the recommended practice is to define theorem environments after cleveref is loaded, I'll structure the preamble so cleveref comes last before the theorem definitions. Now I'm setting up shorthand macros for common number sets like the reals, naturals, and integers. Adding more Spanish-language math operators... I'm also designing a custom title page with a colored rule, bold sans-serif heading, and spacing instead of using the default \maketitle. I'm considering adding a small pgfplots graph, maybe sin(x)/x or a sequence plot, to decorate the title page. I'll go with a full title page followed by a table of contents page before the exercise content starts, since the user wanted something aesthetic and they can always trim it down later. Now I'm moving on to drafting the actual example exercises. I'll start with Section 1 on sequences of real numbers, writing the first exercise as a limit proof by definition for (2n+1)/(n+3) → 2, working through the epsilon-N argument using the Archimedean property to bound 5/(n+3), then begin a second exercise on sequence limits. Confirms the sequence is increasing and bounded, so it converges, and taking limits gives L=2. I'll box this as an application of the monotone convergence theorem, then move to Section 2 on limits and continuity, starting with an ε-δ proof that lim_{x→2} x² = 4, bounding |x+2| by restricting δ ≤ 1 and choosing δ = min{1, ε/5}. Next I'll add Ejercicio 2.2 on continuity: f(x) = x sin(1/x), f(0)=0, showing continuity at 0 via the squeeze theorem and nondifferentiability by exhibiting two sequences h_n giving different difference quotient limits, with a figure showing f bounded by ±|x|. Then I'll begin Section 3 on differentiability. I'll add a nota box explaining o(·) notation. For structure, I'm planning four sections: sucesiones (2 ejercicios), límites y continuidad (2, one with figure), cálculo diferencial (2), and series numéricas with one exercise covering the telescoping sum ∑1/(n(n+1))=1 and a comparison criterion for ∑(n+1)/(n³+2). I'll skip an appendix to keep things concise, and set up an `enumitem` list style for labeled parts like (a), (b) with bold lowercase labels, referencing them in solutions as "Apartado (a)". I'll also include a pgfplots figure of x·sin(1/x). I need to be careful with pgfplots since it defaults to degrees for trig functions, so I'll use `trig format plots=rad` and pick a sample count (800 rather than 801) that avoids landing exactly on x=0 and causing a division error. I'm also thinking about a decorative title page element — maybe a small TikZ/pgfplots drawing showing a smooth curve with a tangent line, or illustrating a sequence like (1+1/n)^n converging to e, to visually tie into the document's theme without overcomplicating things. I'm settling on 11pt with Palatino (via newpx), slightly increased line spacing for readability, and still weighing what sans-serif font to pair for headers since newpx doesn't include one. Actually, simpler to skip the sans font package entirely and just rely on bold Palatino for headings rather than risk package option errors. I'll settle on helvet since it's universally available in base psnfss, rather than biolinum which might not be present on minimal installs. I'll skip extra math alphabet packages like mathalfa since they're not needed here, and will include bm for bold math symbols. For mathtools, I'm using the paired delimiter star variant for automatic sizing with absolute value notation. Microtype should work fine with pdflatex, and I'm confirming tcolorbox's "most" library doesn't load pgfplots so I need to load that separately. For babel, I'm adding the es-tabla option to rename "Cuadro" to "Tabla" and noting that Spanish babel also reformats \today into a full date string. I'm trying to recall the exact decimal point behavior in Spanish babel—whether the es-nodecimaldot option (possibly deprecated) affects how periods behave in math mode versus the decimal comma shorthand commands. Since using es-noshorthands should disable all the active characters including any math-mode dot shortcuts, I'll just avoid decimals or use braces around commas to be safe. I'm also recalling that babel-spanish's spanish.ldf may define trig operator commands like \sen, \tg, \arcsen under a "spanishoperators" option, which could matter if the document uses sine/tangent notation. I'm also trying to recall the various babel-spanish package options like es-nolists, es-noquoting, es-noshorthands, es-notilde, es-minimal, and others that control formatting behavior. I'm piecing together the spanishoperators macro, which redefines Spanish abbreviations for trig and log functions like sen, tg, cosec, cotg, senh, tgh, along with arc-prefixed inverse forms. Math operators are actually controlled through the `\spanishoperators` macro, which I can disable with `\let\spanishoperators\relax` if I don't want babel redefining things like `\sen`. That raises the question of whether a preemptive `\DeclareMathOperator{\sen}{sen}` in the preamble would conflict with babel's own definition later, possibly causing a redefinition clash or error. I recall that spanish.ldf hooks the math operator definitions into `\extrasspanish`, and the documentation mentions a `\spanishoperators` macro listing the defined operators (like \sen, \arcsen, \tg, etc.) which users can redefine if needed. If babel defines operators with `\def`, my own `\DeclareMathOperator{\sen}` could get silently overridden at `\begin{document}`, but since both produce "sen" the output should still be correct regardless of ordering. To avoid a potential "already defined" clash, I'm considering guarding the definition with a check for whether `\sen` already exists before declaring it, so mine only applies if babel hasn't defined it yet. But I also need to think through whether babel's own internal definition mechanism, which redefines operators via its own macro, would conflict with mine at `\begin{document}`. I think `\providecommand{\sen}{\operatorname{sen}}` is the safest bet — it only defines `\sen` if undefined, and babel can then skip or override it safely afterward. I'm trying to recall the actual spanish.ldf source to confirm how it guards against redefinition, picturing something like a conditional check wrapping the operator definitions. Right, the operators are only defined if not already existing, so a user's own definition of \sen would be respected. I'm leaning toward using `\providecommand` as a fallback with a comment, reasoning that it's safe either way: if babel defines the operators at load time, mine does nothing; if babel defines them later only when undefined, mine still wins consistently. The only failure case would be if babel used `\newcommand` at begin-document, which would throw an "already defined" error — but I'm fairly confident that's not how it works, since that would break countless documents. I'll just stick with `\sen` as the key example and skip `\tg` to avoid clutter. I'm also recalling that babel-spanish might already define accented forms like `\lím`, `\máx`, `\mín` for operators, so I should check whether to rely on those built-ins rather than redefine them myself. I also need to load cleveref with the Spanish option so names like "ecuación" and "sección" come out right, then set custom `\crefname` entries for my own environments like "ejercicio" and "teorema," using the capitalized form for references like "Teorema 3.1." For equations I'll just stick with `\eqref` directly rather than fighting cleveref's naming. I'm also confirming that tcolorbox's auto-counter labels work with cleveref since they register as named counters like `tcb@cnt@ejercicio`, so `\cref{ej:nombre}` resolves correctly to "Ejercicio 1.1". Now I'm checking a subtler detail: whether `tcolorbox`'s default `parbox=true` resets `\parskip` inside the box, since the content is placed in a minipage-like context rather than a normal paragraph — switching to `parbox=false` would preserve normal paragraph spacing if needed. So `\@parboxrestore` zeroes out indentation and spacing parameters along with margins and skips, which is what minipage relies on. That means tcolorbox's parbox=true mode likely inherits this zeroed state, while parbox=false preserves the surrounding text's parskip and parindent values instead. With parbox=false, parindent inherits the document's zero value, so the "Solución." label still flows into the first paragraph correctly. I'm leaning toward making parskip slightly flexible (like 0.5em plus 0.1em) for better spacing, and confirming it won't interfere with TOC, lists, or display math since enumitem handles lists separately. I should also double check parindent is set to 0pt globally to match. I'm setting itemize bullets to use the custom blue color via enumitem, and thinking through how section headers appear in the fancyhdr running heads—since `\leftmark` is populated by `\sectionmark`, I want to make sure the uppercase formatting or lack thereof displays section numbers and titles cleanly in the header. I'm also checking page style behavior: `\section` doesn't trigger a page style change in article class, and `\tableofcontents` similarly leaves the current page style untouched, so only the titlepage environment resets it. For the TOC itself, I'm considering whether to rename "Contents" to a Spanish equivalent rather than using titletoc for deeper styling. Now I'm renaming the contents title via babel's caption hook to "Índice" instead of the default "Índice general," then building the titlepage with centered title text in a custom color and font size, followed by a subtitle line. Writing titlepage layout... I'm deciding to leave the table of contents with default formatting rather than forcing new pages before each section, since the document is relatively short and over-structuring could hurt aesthetics. I'll let the user add page breaks manually where needed instead of hardcoding them. I'm also adding a short notation box at the start of the document explaining conventions, like defining the natural numbers set, before moving into the main content. Then I start drafting the actual exercise section on sequences of real numbers, beginning with a formal definition of the limit of a sequence. Next I write a first exercise asking to prove by definition that a given rational sequence converges to 2, followed by the start of a worked solution showing how to bound the absolute difference in terms of epsilon to find the required n0. Eso completa la demostración. Vale la pena notar que no hace falta hallar el $n_0$ óptimo, basta una cota simple y suficiente. Ahora paso a enunciar el teorema de la convergencia monótona: toda sucesión monótona y acotada converge, y si es creciente y acotada superiormente, su límite coincide con el supremo del conjunto de sus términos. Después planteo un ejercicio sobre una sucesión definida por recurrencia ($a_1=1$, $a_{n+1}=\sqrt{2+a_n}$), pidiendo probar que está acotada entre 0 y 2, que es estrictamente creciente, y deducir su convergencia y límite. Empiezo la solución abordando el primer apartado, la acotación. Esa factorización se cumple porque, por (a), sabemos que $-10$. Así, concluyo que $L=2$ y pienso en cómo resaltar visualmente este resultado final usando un cuadro de color con tcolorbox. Defining the result box command... Ahora empiezo a redactar la sección 2, dedicada a límites y continuidad de funciones, comenzando con el primer ejercicio etiquetado. Estoy planteando la demostración epsilon-delta: fijado $\eps>0$, factorizo $x^2-4$ como $(x-2)(x+2)$ para acotar cada factor por separado y determinar el $\delta$ adecuado. Imponiendo primero $\abs{x-2}<1$, acoto $\abs{x+2}<5$, y tomando $\delta=\min\{1,\eps/5\}$ obtengo que $\abs{x^2-4}<\eps$ cuando $0<\abs{x-2}<\delta$, completando así la demostración. Ahora pienso en agregar una nota explicando la estrategia general de este tipo de argumento para generalizarlo a otros casos similares. Con T1 y utf8, newpxtext soporta directamente los caracteres « y » (vía `\guillemotleft`/`\guillemotright`), así que puedo definir `\cita` usando esos símbolos tipográficos directamente en el código fuente sin necesidad de atajos como `<<`. Ahora estoy redactando el ejercicio 2.2 sobre continuidad y derivabilidad, planteando la función a trozos con $x\sen(1/x)$ para $x\neq 0$ y $0$ en el origen, pidiendo estudiar ambas propiedades en $x=0$. Para la figura que acompaña la solución, como no se pueden usar floats dentro de cajas, opto por un `tikzpicture` dentro de un `center` junto con `\captionof{figure}` del paquete `caption`, configurando el estilo de las etiquetas con color azul principal. Ahora redacto la demostración de continuidad de $f$ en $x=0$: para $x\neq 0$ acoto $|\sen(1/x)|\le 1$, obtengo $|f(x)-f(0)|\le |x|\to 0$, y concluyo por el criterio del emparedado que el límite es $0=f(0)$, estableciendo la continuidad. Añado que $f$ es continua en todo $\R$ porque fuera de $0$ es producto y composición de funciones continuas, y planteo un esquema con tikzpicture para dibujar la gráfica de la función. I'm checking whether 1200 samples near x=0 will cause precision issues, since 1/x grows to values like 3000 radians where pgfplots' FPU needs to reduce the angle modulo 360 degrees—worth confirming the FPU has enough precision to keep the oscillation accurate at that scale. With 6 significant digits of precision, the degree error stays around ±1, which is fine since this is just decoration—so I'll avoid `smooth` to prevent spline overshoot and pick a domain/sample count that keeps x=0 from ever being sampled exactly, which it does cleanly here. For ticks, I want decimal commas instead of dots to match Spanish conventions, so I'll add a pgfplots number format setting for that. Then for the derivability section, I'm computing the incremental quotient at 0, showing that it simplifies to sin(1/h), and I'll use this to argue about the limit's behavior as h approaches zero. $f$ no es derivable en $0$. Ahora paso a la siguiente sección, sobre cálculo diferencial, donde voy a enunciar el teorema del valor medio de Lagrange: si $f$ es continua en $[a,b]$ y derivable en $(a,b)$, entonces existe un punto intermedio $c$ donde la derivada iguala la pendiente media de la función en el intervalo. Luego planteo un ejercicio aplicando este teorema: demostrar que la función seno es Lipschitz con constante 1, es decir, que $|\sen x - \sen y| \le |x-y|$. Para la solución, separo el caso trivial $x=y$ del caso $x

generame un Latex con buen diseño para un documento de resol...