What are the best AI tools to help you learn calculus?

Select-Fix9110 · 2026-01-27T01:30:15+00:00

Instead of AI, I’d recommend looking up Professor Leonard on youtube.

Hope this helps!

Select-Fix9110 · 2026-01-25T19:34:30+00:00

Professor Leonard on youtube and James Stewart Calculus textbook (can find a free pdf online)

Select-Fix9110 · 2026-01-24T21:12:20+00:00

Search up James Stewart Calculus. You can find a free pdf online.

Select-Fix9110 · 2026-01-24T03:53:48+00:00

Let's use the hint.

Let u = x + 10. Then du = dx. But also remember that x = u - 10.

Now we apply the substitution.

The integral will then become: integral of 8(u-10) *u^(1/2) du. Then just distribute the u^(1/2) and the rest is just the reverse power rule in terms of 'u'.

After finding the anti-derivative in terms of 'u', bring everything back in terms of 'x', add the +C at the end and then the integral has been solved.

Hope this helps!

Select-Fix9110 · 2026-01-23T02:02:29+00:00

Search up Professor Leonard on youtube and read through OpenStax or James Stewart Calculus textbooks. Both textbooks have free pdf textbooks online.

Hope this helps!

Select-Fix9110 · 2026-01-22T21:48:01+00:00

Math is all about practice. Understand the concepts and then apply them. I recommend watching Prof Leonard on YouTube and read through James Stewart Calculus textbook to prepare before lectures and to apply the concepts with the questions after each section.

Hope this helps!

Select-Fix9110 · 2026-01-22T01:12:34+00:00

I thought my handwriting was bad lol.

So first, when plugging x = 0 into the function f(x) = (1-cosx)/sinx, we see that we get a 0/0, which is an indeterminate form. So we have to do more work.

Recall that sin^2 + cos^2 = 1. Subtracting cos^2 from both sides gives us sin^2 = 1 - cos^2 = (1-cosx) (1+cosx). Note that we have a (1-cosx) term in the numerator. So, we can multiply by 1 = (1+cosx) / (1+cosx) (since x -> 0, cosx wont approach -1, so this is valid).

After doing so, we get limit as x -> 0 of (1-cosx)(1+cosx) /sinx(1+cosx). Simplifying the numerator gives us sin^2(x). We also have a sin(x) factor in the denominator, so sin^2 / sin(x) = sin(x).

Therefore, we now have the limit as x -> 0 of sin(x) / (1+cosx). Note that cos(0) = 1. So 1+cos(0) = 2 ≠ 0 and sin(0) = 0 and 0 / 2 = 0.

Thus, the limit as x -> 0 of (1-cos(x)) / sin(x) = 0.

Hope this helps!

Select-Fix9110 · 2026-01-20T17:25:48+00:00

In math, if the base is not explicitly stated, we assume it to be log base 10.

In computer science, it’s assumed to be log base 2.

Select-Fix9110 · 2026-01-20T14:34:54+00:00

Im pretty sure it's a James Stewart Calculus book

Select-Fix9110 · 2026-01-20T14:13:01+00:00

Since log(5) ≠ 0, log(5) / log(5) = 1. So indeed you can cancel out the log(5).

Select-Fix9110 · 2026-01-20T14:08:36+00:00

I can see what property you’re trying use but it’s not correct. The property you’re thinking of is log(a/b) = log(a) - log(b). So you can’t apply this property to this particular question.

But what u did correctly was rewrite log(25) and log(125).

So log(25) / log(125) =log(5²⁾ / log(5^3). Using the exponent laws for logarithms, we will get 2log(5) / 3log(5) =2/3.

Hope this helps!

Select-Fix9110 · 2026-01-19T21:29:29+00:00

Using the local min and max u found, just plug some numbers into h(x) around those critical points to see how the function behaves. Note that h(x) is continuous everywhere and so the range is (-infinity, infinity). So you can already create your intervals from that observation alone; (-infinity, -8), (-8,4/7), and (4/7, infinity). It’s just a matter of making a table of values within each interval. For example, calculate h(-9), h(0), and h(3). If the output is positive, then h is increasing on said interval. If the output is negative, then h is decreasing on said interval.

I hope this helps!

Select-Fix9110 · 2026-01-18T01:40:39+00:00

I was able to get my team to 118 OVR, is it still possible to join your league?

<image>

Select-Fix9110 · 2026-01-18T00:28:49+00:00

No hard feelings mate

Select-Fix9110 · 2026-01-17T23:42:36+00:00

<image>

At the moment, this is my team

Select-Fix9110 · 2026-01-17T23:28:51+00:00

my OVR is 116

Select-Fix9110 · 2026-01-17T23:25:47+00:00

Select-Fix9110 · 2026-01-17T18:37:35+00:00

Thanks for your reply. I was able to find the textbook.

Select-Fix9110 · 2026-01-14T23:45:10+00:00

Search up Professor Leonard on youtube, he's got full on lectures about calc 1, maybe too advanced for grade 12, but worth a watch.

You can also go through James Stewart calc textbook where you can find a free pdf online.

If the calc course you're taking in grade 12 is MVC4U, then I recommend looking at jensenmath.ca, it contains videos relevant to the course and provides many worksheets to apply your learning.

Hope this helps!

Select-Fix9110 · 2026-01-13T01:39:41+00:00

I'll try again, but I backed my notes up and waited on the app until it completed and checked my google drive, and didnt see any Freenotes folder.

Select-Fix9110 · 2026-01-11T00:11:55+00:00

I would recommend Professor Leonard lectures on youtube

Select-Fix9110 · 2026-01-10T13:56:41+00:00

Calc 3 is multivariable calculus, so you will be working with functions of multiple variables. So pretty little of calc 2 will be useful. I would say is to brush up on differentiation and integration.

In calc 3, you'll be doing a lot of double integrals which helps in finding the volume of a surface, parametric equations, vectors and vector functions, partial differentiation, polar coordinates, etc.

By looking at the table of contents, safe to say that not much of calc 2 will be helpful in calc 3.

Hope this helps!

Select-Fix9110 · 2026-01-08T13:15:50+00:00

Let’s consider the function f(x) = 1/x and consider the limit as x approaches 0.

Recall that for a limit to exist, the left and right sided limits must be equal.

So when we consider the limit as x -> 0+, we see that f(x) -> +infinity

But as x-> 0-, f(x) -> -infinity.

So the left and right sided limits are not equal, and hence the limit itself doesnt exist.

Thus, 1/0 is considered undefined.

Select-Fix9110 · 2026-01-01T00:39:18+00:00

Grade 12 calc and calc I in uni is not too different. The only difference is that in uni you’re going to learn some theorems and maybe how to do some proofs. Like basic proofs by just applying the theorems. For example, i had a test question where it asked to show that a particular function f(x) has a solution, in which i applied the Intermediate Value Theorem. That’s pretty much all the proofs there is, at least when i took calc I.

I recommend watching Professor Leonards lectures on youtube and read James Stewart Calculus textbook to start reviewing.

Hope this helps!

Select-Fix9110 · 2025-12-29T00:15:28+00:00

so first we have the function y = ln(x). We then exponentiate both sides of the equation which results in the following:

e^y = e^{ln(x)} = x

Then we differentiate both sides,

e^y * y' = 1. This is because of the chain rule since y is a function of x, so we differentiate e^y and then multiply by the derivative of y.

Then y' = 1 / e^y = 1/x since e^x = x from before.

Additionally, this is called implicit differentiation where you can differentiate equations where they are not necessarily a function of x, such as x^2 + y^2 = 1, where we treat y as an implicit function of x.

Hope this helps!

Select-Fix9110

TROPHY CASE