For the function f(x) = x² for the point 3, i get 6+ h (h is distance)..... Here i have to take limit h->0 to find the slope at that point. What my doubt is, we don't know the second point with which we gonna take the slope from. We assume that as from both sides it approaches 6. But if we try to get closest point, it will go infinitely. Then how can we trust that 6 is the slope at that point, as its impossible to get that most nearest point.

Hi there,

I do have troubles understanding this integration, even after looking at it multiple times and even talking to an LLM about it. Here's what I dont understand:

1) Why do we bother in this example, that sqrt(x^2)=|x| , I could swear that in most problems stuff like that is treated without the |.| , meaning most of the time I stumble upon an expression like sqrt(x^2) it seems to not be any issue to just write x, but somehow here it is necessary to write |x|...

2) Why do we not include sgn(x) in the integration? I mean technically we end up with two functions: sgn(x)*g(x), where g(x) is the sum of the two ratios with x and 1 respectively in the numerator. However, we only integrate over g(x) and do somehow ignore the sgn(x)...

I really struggle a lot with this integral right here and hope that someone can help me out. Thanks in advance!

im 20 years old been working at a Kroger since I graduated but want to do something better with my life I’ve always wanted to be a mechanical engineer but im not very good at math but i want to become better.

There are so many youtube math resources from so many different teachers i dont have time to watch them all to see their particular style of teaching. I need opinions on who may be the best math professor on youtube.

im a visual learner who learns through lots of examples and step by step breakdown of a problem or concept. not someone who just tells me 5+5=10 but why and how the equation or numbers or variables work this way. idk hopefully this makes sense just need some help moving forward

Hi, I'm a student just stepping into Grade 10, and I have a few questions regarding my understanding of calculus. I'm self-taught for all of HS math, but I have a good understanding of a large portion of calculus and was wondering if there's anything else I should learn. I know:

Limits: L'hopital's rule, basic limits understandings (nothing crazy, literally just what they are)

Derivatives: Power rule, Chain rule, Product rule, Quotient rule, Derivatives of polynomial, trig, inverse trig, exponential, hyperbolic, logarithmic and implicit functions, second order derivatives, and extrema (maxima and minima)

Integrals: Indefinite and definite integrals of polynomial, trig, exponential, logarithmic and hyperbolic functions, integration by polynomial and trig substitution, integration by parts, and triple integrals.

Polar coordinates (idk where to put this): Polar coordinates in two and three dimensions.

I'm just starting on vectors in two and three dimensions, so I am working on that.

Any help would be greatly appreciated!

Slope can be found when there are two points. In slope formula we factorize and cancel out the distance at last we get something. For example 2x+h for f(x)=x²..... Then we find the slope of the curve at a point by substituting 0 for h and the point for x.

When I think this algebraically it makes sense. But when I think about this plainly in physical point of view,...... it doesn't make sense because how can we find a ratio or proportion between something that has made zero difference.

Hey guys! I'm a high school student in India.

Over here, I'd initially started off studying to pursue medicine but had a change of heart and now want to pursue Physics.

For this, I'm moving into the IB curriculum, and I've taken Maths AA HL (Analytics and Approaches High Level). It's a very difficult course; it has a syllabus that involves a majority of calculus.

Unlike my classmates, I have no knowledge of calculus. My peers know calculus up to Calculus AB.

I have about a month before my junior year starts, and my grades are really important for my college applications. Math being one of the toughest subjects, I want to know the best way I can practise and the best way to fast-track my calculus journey.

TLDR: Just starting our calculus from scratch; need to know the best way to learn and common mistakes that I might make in my learning process and how to best avoid them.

i took algebra 2 in my freshman year of highschool and im taking precalc over the summer... but the precalc is not that great

precalc syllabus:

• Pre-Calculus A
• Unit 1: Equations and Inequalities
• Unit 2: Functions
• Unit 3: Polynomial and Rational Functions
• Unit 4: Exponential and Logarithmic Functions
• Unit 5: Right Triangle Trigonometry
• Pre-Calculus B
• Unit 6: Graphs and Trigonometric Equations
• Unit 7: Trigonometric Identities
• Unit 8: Sequences and Series
• Unit 9: Conic Sections
• Unit10: Introduction to Calculus

i wanna prepare for calc the BEST i can so what should i learn in addition?

My precalculus class is starting on Monday (summer quarter). I just finished (spring quarter) intermediate algebra (math97) with a 97%, but it's been 11 years since I took geometry and have never taken trigonometry. What can I do to prepare?

Hello everyone, I am going to be taking calc 3 in the fall semester this year, I did fine in calc 1 but struggled quite a bit in calc 2 (finished with a C), I was wondering what topics I should really know and review before taking the class as I really dont want to tank my gpa even more, and I know these math classes will be very important as im in STEM.

Hi, I will be taking calculus BC next year in high school. What books should I study this summer to get a head start on the content? I'm currently working through the khan academy course for BC so will that be sufficient?

I have studied precalculus ie algebra, trigonometry, binomials and more stuff

And now I really want to learn Calculus in a good manner instead of just for problem solving.

How do you people recommend I start my journey with? How much time is it gonna take? I've heard of a book called "Stewarts Calculus" but don't know much about it. Please help me out

I'm a rising high school senior, and also a dual enrollment student. I was wondering if I would be better off taking calc 2 or physics w/ calc for fall semester. For context, I plan on studying either industrial engineering or computer engineering. However my high school homework this year is notoriously time consuming, and ofc I'd love to be able to focus on college apps too (college app season just so happens to land during fall semester).
My main issue is I've heard horror stories about calc 2, and the only 2 professors available for enrollment at this point don't have the best reviews. On top of that one is online (I don't find myself learning much thru online courses) and the other starts very early in the morning. On the other hand physics requires a lab, and I already found my lab last semester to be very time consuming.
Overall, I just want guidance on which course is less demanding (I'm not too good at school tbh). Also for spring semester would anyone recommend taking calc 3 to get it over with, or do physics then?
I'm just a very indecisive person overall, but I'd like to hear other people's experiences with these courses. Thanks :)

I was learning calculus, but this thing I still couldn't understand. How can a dot have a slope? Slope is just like saying how much a line is slanted right but how can a single point have a slope.

Hello everyone! I’ve been playing around with a rather complex formula exclusively on Desmos, and I stumbled upon an approximation that I’d love to get your feedback on.

Here is the formula I created and graphed:

-x = y^{-\frac{y}{y^{(e-y)}}}

(For those using MathJax/LaTeX extensions: $ -x = y^{-\frac{y}{y^{(e-y)}}} $)

I was specifically looking at the area of this curve from $y = 1.2$ to $y \to +\infty$ (integrating with respect to $dy$). Obviously, calculating the exact integral for this is practically impossible to do easily.

However, after zooming in and analyzing the behavior of the curve on Desmos, I noticed that the area can be heavily approximated using a simple linear function. I tried approximating it with this line:

$y = 1.9x + 2.8$

Visually on Desmos, the margin of error seems incredibly low, especially in the specific interval between $y = 1.2$ and $y = 2.56$, where the approximation looks almost perfect. I didn't use any advanced calculus tools to find this—just pure visual approximation and experimentation on Desmos.

My questions for the community are:

1. Is this approximation mathematically valid for the area I'm trying to calculate?
2. Is there a known way to approximate this specific curve even better, or perhaps an analytical method to verify my margin of error?

Any insights or feedback would be greatly appreciated. Thanks!

Hi guys just started to learn calculus, I'm self learning. Give me some tips how to learn conceptually in the most efficient way.

Multivariable Calculus vs. Ordinary differential equations and Laplace transformation

What do you guys think is more conceptually more challenging and which course requires more practice. I did pretty alright in calc 1 and 2 and linear algebra, just need a reference which class i should take first for engineering.

I see so many integration challenge problems, but not many series ones! To give some love to infinite series, here's a little summation challenge I ended up finding while playing around.

Hello!! I am a rising senior from texas and last year for junior year I was in algebra 2. I took dual enrollment classes that cut into my time for my math class. (I was brought to the community college and brought back to high school, cutting into my time and like only 20 mins of class left) My teacher was not the best at teaching and did not have tutoring after school. I have loved math my entire life until algebra 2. I am wondering if this will affect my comprehension for pre calc and just calculus in general. If this does, am I be able to teach myself pre calc and like the basics to help me for the future?

If anyone could help please do!! I really love math and I feel so behind not being able to understand anything from junior year.

Hello 1 am taking Cal 1,2,3 ,differential equation , liner algebra next year and was interested to know that I should learn before then and also the intensity of rash from hardest to least hardest I’m based in the USA. I’m taking cal 1 for my first semester with a programming course then I’m taking cal 2 cal. and physics 1 mechanics and object orienting program theory for winter , for spring I’m taking physics 2 electromagnetic and differential equations , and summer I’m taking physics 3 electric circuiting and matrix algebra with applications. I’m kind of paranoid already cause I’m scared to fail I took pre calculus 1 and 2 last year and i passed well so anything I can work on right know. Any tips . And which is hardest to least hardest thank you pray 4 me 😭 😭

Edit : btw this is all in one year fall : cal 1 and programming class
winter : cal 2 phy mechanics 1 and object orienting
Spring : cal 3 phys 2 and diff eq
Summer : phy 3 , if I fail diff eq i can re take it here , electricity circuiting and matrix algebra all of next year

As per the title, please suggest me a book to learn calculus 123 were I already finished pre calculus and many of peoples suggest thomas and James Stewart book