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Here are a number of examples of Calculus problems that ChatGPT was not able to solve satisfactorily (at least now, but it may learn!)

(Edit: Here is another thought, different from my original response posted below: GPT at its current stage of development is pretty bad in solving mathematics problems, as demonstrated by examples posted below and many other examples that I did not post here. It needs further development. But, assuming that it improves, at some point in the future we will see the possibility of administering homework and exams on GPT itself, in such a way that GPT is the proctor and if a student tries to ask GPT to solve a problem that is a homework or exam problem, GPT will be able to recognize that and will remind the student that this is his homework or exam and must be solved by the student.)

Here are a number of examples of Calculus problems that ChatGPT was not able to solve satisfactorily (at least now, but it may learn!)

Here are a number of examples of Calculus problems that ChatGPT was not able to solve satisfactorily (at least now, but it may learn!)

Example 1) (Use large numbers) Explain how you would integrate $\int\sin^{679}(x) dx$, but don't find the answer.

The successful solution by a student is to separate one $\sin(x)$, then write the remaining $\sin^{678}(x)$ as $(\sin^2(x))^{339}$, which is equal to $(1-\cos^2(x))^{339}$ and then say use the substitution $u=\cos(x)$, although the answer to that integral will be very complicated and long.

Here is ChatGPT's response to the same question:

Example 2) Suppose the series $\sum_{n=1}^\infty a_n^2$ is convergent. What can we say about the convergence or divergence of the series $\sum_{n=1}^\infty \frac{a_n^2}{n}$?

The successful solution by a student will use the Comparison Test, as $0\leq \frac{a_n^2}{n}\leq a_n^2$ and conclude that the series $\sum_{n=1}^\infty\frac{a_n^2}{n}$ is convergent.

Here is ChatGPT's response to the same question (note that the conclusion is correct but the reasoning doesn't make sense):

Example 3 (Include extraneous information) Suppose $f$ is a continuous function and $g(x)=\int_1^x f(t)dt$. If $f(4)=0$ and $f(5)=1$ can we find a critical number of $g(x)$?

The successful solution by a student is to say since $f$ is continuous, $g$ is differentiable and $g^\prime(x)=f(x)$. Since $g^\prime(4)=f(4)=0$, $x=4$ is a critical number of $g$. That $f(5)=1$ is irrelevant.

Here is ChatGPT's response to the same question, which does not make sense:

Example 4 suppose $f(x) = x+3$ when $x\leq-2$, and $f(x) = -x/2$ when $-2<x<2$ and $f(x) = x-3$ when $x\geq2$. Suppose $g(x)=\int_{-4}^x f(t)dt$. Can we find the extreme values of $g$ on the interval $[-4,6]$?

The successful solution by a student would use the Closed Interval Method. As $f$ is continuous, $g^\prime(x)=f(x)$ and $g$ has critical numbers at $x=-3,0,3$. To find the extreme values of $g$ on the interval $[-4,6]$ it suffices to find and compare the values of $g(-4), g(-3), g(0), g(3)$ and $g(6)$.

Here is ChatGPT's response to the same question, which doesn't make sense (it actually got stuck for more than 5 minutes there):

Since ChatGPT got stuck in the middle of solving this problem, I stopped it and asked it to regenerate its response. In its new response, somewhere it said that $-3$ is not in the interval $[-4,6]$! So I challenged it and here is the conversation that followed:

Note that it is still saying $-3$ is not in the open interval $(-4,6)$!

Example 5 Is it possible to integrate $\frac{x}{\sqrt{9-x^2}}$ using integration by parts?

ChatGPT got stuck again in the middle of solving the problem:

Example 6 Here is an elementary question: Can a rectangle and a circle have the same area?

Here is ChatGPT's response:

Here are a number of examples of Calculus problems that ChatGPT was not able to solve satisfactorily (at least now, but it may learn!)

Example 1) (Use large numbers) Explain how you would integrate $\int\sin^{679}(x) dx$, but don't find the answer.

The successful solution by a student is to separate one $\sin(x)$, then write the remaining $\sin^{678}(x)$ as $(\sin^2(x))^{339}$, which is equal to $(1-\cos^2(x))^{339}$ and then say use the substitution $u=\cos(x)$, although the answer to that integral will be very complicated and long.

Here is ChatGPT's response to the same question:

Example 2) Suppose the series $\sum_{n=1}^\infty a_n^2$ is convergent. What can we say about the convergence or divergence of the series $\sum_{n=1}^\infty \frac{a_n^2}{n}$?

The successful solution by a student will use the Comparison Test, as $0\leq \frac{a_n^2}{n}\leq a_n^2$ and conclude that the series $\sum_{n=1}^\infty\frac{a_n^2}{n}$ is convergent.

Here is ChatGPT's response to the same question (note that the conclusion is correct but the reasoning doesn't make sense):

Example 3) (Include extraneous information) Suppose $f$ is a continuous function and $g(x)=\int_1^x f(t)dt$. If $f(4)=0$ and $f(5)=1$ can we find a critical number of $g(x)$?

The successful solution by a student is to say since $f$ is continuous, $g$ is differentiable and $g^\prime(x)=f(x)$. Since $g^\prime(4)=f(4)=0$, $x=4$ is a critical number of $g$. That $f(5)=1$ is irrelevant.

Here is ChatGPT's response to the same question, which does not make sense:

Example 4) suppose $f(x) = x+3$ when $x\leq-2$, and $f(x) = -x/2$ when $-2<x<2$ and $f(x) = x-3$ when $x\geq2$. Suppose $g(x)=\int_{-4}^x f(t)dt$. Can we find the extreme values of $g$ on the interval $[-4,6]$?

The successful solution by a student would use the Closed Interval Method. As $f$ is continuous, $g^\prime(x)=f(x)$ and $g$ has critical numbers at $x=-3,0,3$. To find the extreme values of $g$ on the interval $[-4,6]$ it suffices to find and compare the values of $g(-4), g(-3), g(0), g(3)$ and $g(6)$.

Here is ChatGPT's response to the same question, which doesn't make sense (it actually got stuck for more than 5 minutes there):

Since ChatGPT got stuck in the middle of solving this problem, I stopped it and asked it to regenerate its response. In its new response, somewhere it said that $-3$ is not in the interval $[-4,6]$! So I challenged it and here is the conversation that followed:

Note that it is still saying $-3$ is not in the open interval $(-4,6)$!

Example 5) Is it possible to integrate $\frac{x}{\sqrt{9-x^2}}$ using integration by parts?

ChatGPT got stuck again in the middle of solving the problem:

Example 6) Here is an elementary question: Can a rectangle and a circle have the same area?

Here is ChatGPT's response:

Here are a number of examples of Calculus problems that ChatGPT was not able to solve satisfactorily (at least now, but it may learn!)

Example 1) (Use large numbers) Explain how you would integrate $\int\sin^{679}(x) dx$, but don't find the answer.

The successful solution by a student is to separate one $\sin(x)$, then write the remaining $\sin^{678}(x)$ as $(\sin^2(x))^{339}$, which is equal to $(1-\cos^2(x))^{339}$ and then say use the substitution $u=\cos(x)$, although the answer to that integral will be very complicated and long.

Here is ChatGPT's response to the same question:

Example 2) Suppose the series $\sum_{n=1}^\infty a_n^2$ is convergent. What can we say about the convergence or divergence of the series $\sum_{n=1}^\infty \frac{a_n^2}{n}$?

The successful solution by a student will use the Comparison Test, as $0\leq \frac{a_n^2}{n}\leq a_n^2$ and conclude that the series $\sum_{n=1}^\infty\frac{a_n^2}{n}$ is convergent.

Here is ChatGPT's response to the same question (note that the conclusion is correct but the reasoning doesn't make sense):

Example 3 (Include extraneous information) Suppose $f$ is a continuous function and $g(x)=\int_1^x f(t)dt$. If $f(4)=0$ and $f(5)=1$ can we find a critical number of $g(x)$?

The successful solution by a student is to say since $f$ is continuous, $g$ is differentiable and $g^\prime(x)=f(x)$. Since $g^\prime(4)=f(4)=0$, $x=4$ is a critical number of $g$. That $f(5)=1$ is irrelevant.

Here is ChatGPT's response to the same question, which does not make sense:

Example 4 suppose $f(x) = x+3$ when $x\leq-2$, and $f(x) = -x/2$ when $-2<x<2$ and $f(x) = x-3$ when $x\geq2$. Suppose $g(x)=\int_{-4}^x f(t)dt$. Can we find the extreme values of $g$ on the interval $[-4,6]$?

The successful solution by a student would use the Closed Interval Method. As $f$ is continuous, $g^\prime(x)=f(x)$ and $g$ has critical numbers at $x=-3,0,3$. To find the extreme values of $g$ on the interval $[-4,6]$ it suffices to find and compare the values of $g(-4), g(-3), g(0), g(3)$ and $g(6)$.

Here is ChatGPT's response to the same question, which doesn't make sense (it actually got stuck for more than 5 minutes there):

Since ChatGPT got stuck in the middle of solving this problem, I stopped it and asked it to regenerate its response. In its new response, somewhere it said that $-3$ is not in the interval $[-4,6]$! So I challenged it and here is the conversation that followed:

Note that it is still saying $-3$ is not in the open interval $(-4,6)$!

Example 5 Is it possible to integrate $\frac{x}{\sqrt{9-x^2}}$ using integration by parts?

ChatGPT got stuck again in the middle of solving the problem:

Here are a number of examples of Calculus problems that ChatGPT was not able to solve satisfactorily (at least now, but it may learn!)

Example 1) (Use large numbers) Explain how you would integrate $\int\sin^{679}(x) dx$, but don't find the answer.

The successful solution by a student is to separate one $\sin(x)$, then write the remaining $\sin^{678}(x)$ as $(\sin^2(x))^{339}$, which is equal to $(1-\cos^2(x))^{339}$ and then say use the substitution $u=\cos(x)$, although the answer to that integral will be very complicated and long.

Here is ChatGPT's response to the same question:

Example 2) Suppose the series $\sum_{n=1}^\infty a_n^2$ is convergent. What can we say about the convergence or divergence of the series $\sum_{n=1}^\infty \frac{a_n^2}{n}$?

The successful solution by a student will use the Comparison Test, as $0\leq \frac{a_n^2}{n}\leq a_n^2$ and conclude that the series $\sum_{n=1}^\infty\frac{a_n^2}{n}$ is convergent.

Here is ChatGPT's response to the same question (note that the conclusion is correct but the reasoning doesn't make sense):

Example 3 (Include extraneous information) Suppose $f$ is a continuous function and $g(x)=\int_1^x f(t)dt$. If $f(4)=0$ and $f(5)=1$ can we find a critical number of $g(x)$?

The successful solution by a student is to say since $f$ is continuous, $g$ is differentiable and $g^\prime(x)=f(x)$. Since $g^\prime(4)=f(4)=0$, $x=4$ is a critical number of $g$. That $f(5)=1$ is irrelevant.

Here is ChatGPT's response to the same question, which does not make sense:

Example 4 suppose $f(x) = x+3$ when $x\leq-2$, and $f(x) = -x/2$ when $-2<x<2$ and $f(x) = x-3$ when $x\geq2$. Suppose $g(x)=\int_{-4}^x f(t)dt$. Can we find the extreme values of $g$ on the interval $[-4,6]$?

The successful solution by a student would use the Closed Interval Method. As $f$ is continuous, $g^\prime(x)=f(x)$ and $g$ has critical numbers at $x=-3,0,3$. To find the extreme values of $g$ on the interval $[-4,6]$ it suffices to find and compare the values of $g(-4), g(-3), g(0), g(3)$ and $g(6)$.

Here is ChatGPT's response to the same question, which doesn't make sense (it actually got stuck for more than 5 minutes there):

Since ChatGPT got stuck in the middle of solving this problem, I stopped it and asked it to regenerate its response. In its new response, somewhere it said that $-3$ is not in the interval $[-4,6]$! So I challenged it and here is the conversation that followed:

Note that it is still saying $-3$ is not in the open interval $(-4,6)$!

Example 5 Is it possible to integrate $\frac{x}{\sqrt{9-x^2}}$ using integration by parts?

ChatGPT got stuck again in the middle of solving the problem:

Example 6 Here is an elementary question: Can a rectangle and a circle have the same area?

Here is ChatGPT's response: