Gauth vs ChatGPT for Math Homework

Read that table honestly and ChatGPT wins most of it, including the free tier, the apps, and everything outside mathematics. The two rows that go to Gauth are about predictability rather than power: one shape of answer, and nothing to set up before you get it.

Gauth. First solution free with no account. Free accounts get three solutions a day. Gauth Plus is $11.99 a month with a three-day free trial, $31.99 a quarter, or $99.99 a year, as of September 2026. Follow-ups do not consume quota. See the pricing page.

ChatGPT. The free tier allows unlimited everyday text chats, subject to abuse guardrails, with separate caps on file uploads, image generation, voice, deep research, and data analysis. OpenAI says ads may appear on the free and Go tiers in certain countries. Paid plans as of September 2026 are Go at $8 a month, Plus at $20 a month, and Pro from $100 a month, with a $200 tier above that for the largest usage limits. All are billed monthly; OpenAI lists annual billing only for Business and Enterprise. Higher tiers buy more messages on the stronger models, longer reasoning, and tools like agent mode and deep research rather than better arithmetic.

For a student who only needs mathematics, the honest comparison is between free and $11.99 a month, and free is a strong offer. Gauth Plus makes sense if the predictable format and the always-attached reasoning are worth the money to you, not because the free chatbot cannot do the math.

Take ${\lim }_{x\to 0}\frac{\sin 3x}{\tan 5x}$. Substituting zero gives $0/0$, so the expression has to be rewritten before it means anything. The answer is $3/5$, and there are at least three legitimate routes to it: standard small-angle limits, series expansion, or L'Hôpital's rule.

ChatGPTwill almost certainly get 3/5, and often with a good explanation. The variance is in everything else. Ask casually and you may get three lines ending in the answer. Ask again and you may get a full treatment with the standard limits justified. The free tier defaults to a fast model rather than a reasoning one, and a fast answer is where a dropped factor of 5 is most likely to slip past. It may reach for L'Hôpital, which works here, or for the standard limits, which is what most courses want to see. None of that is wrong — it is simply not decided in advance, so you have to read the output critically each time rather than skimming a familiar layout.

Gauth is duller and that is the point. It states the indeterminate form first, converts $\tan 5x$ into sine over cosine so the standard limits can be used, manufactures $\frac{\sin u}{u}\to 1$explicitly rather than asserting it, and finishes with the ratio 3/5 in rendered notation. The follow-up you will actually want — "why is $\tan 5x\approx 5x$allowed near zero?" — sits in the same thread, and if the whole idea of an indeterminate form is shaky, limits and continuity, intuition first is the place to repair it.

Start with the mathematics itself, because pretending otherwise would be dishonest. On long, unusual, or proof-shaped problems — show that a sequence converges, decide whether a series test applies, reason about a counterexample — a frontier model with its reasoning effort turned up is excellent, and it is better than a solver at problems that are mostly argument and only incidentally computation. On a paid tier it can also write and run code to verify a numeric result, which is a form of self-checking Gauth does not have.

Then there is everything that is not mathematics. One subscription covers your essay draft, your code that will not compile, the Spanish translation, the revision timetable, and the reading you did not do. It remembers context across conversations, takes a PDF of your lecture notes as input, generates images, and holds a spoken conversation while you walk to campus. Buying a separate tool for each of those is not a serious plan for most students.

The free tier is the third argument and it is a strong one. Unlimited everyday text chats, on a capable model, at no cost, with the option to push a harder question through a deeper reasoning pass. Gauth's free allowance is three solutions a day. If your budget is genuinely zero and you are willing to prompt carefully, ChatGPT gives you more help per month than we do, and it does it from apps on every device we do not support.

The one thing worth watching is not capability but breadth of temptation. A tool that will also write the reflection essay makes the boundary between studying and outsourcing much easier to cross without deciding to, which is why a concrete test for where that line sits is more useful than a policy. Used deliberately, ChatGPT is the most capable study tool on this list.