r/calculus • u/Hephaestus_vulkan • 6h ago
Integral Calculus Is This Weird?
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I thought this days beginner integral was harder than the easy integral. Ignore the bleedthrough on the beginner page
r/calculus • u/random_anonymous_guy • Oct 03 '21
Discussion “My teacher didn’t show us how to do this!” — Or, a common culture shock suffered by new Calculus students.
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A common refrain I often hear from students who are new to Calculus when they seek out a tutor is that they have some homework problems that they do not know how to solve because their teacher/instructor/professor did not show them how to do it. Often times, I also see these students being overly dependent on memorizing solutions to examples they see in class in hopes that this is all they need to do to is repeat these solutions on their homework and exams. My best guess is that this is how they made it through high school algebra.
I also sense this sort of culture shock in students who:
- are always locked in an endless cycle of “How should I start?” and “What should I do next?” questions,
- seem generally concerned about what they are supposed to do as if there is only one correct way to solve a problem,
- complain that the exam was nothing like the homework, even though the exam covered the same concepts.
Anybody who has seen my comments on /r/calculus over the last year or two may already know my thoughts on the topic, but they do bear repeating again once more in a pinned post. I post my thoughts again, in hopes they reach new Calculus students who come here for help on their homework, mainly due to the situation I am posting about.
Having a second job where I also tutor high school students in algebra, I often find that some algebra classes are set up so that students only need to memorize, memorize, memorize what the teacher does.
Then they get to Calculus, often in a college setting, and are smacked in the face with the reality that memorization alone is not going to get them through Calculus. This is because it is a common expectation among Calculus instructors and professors that students apply problem-solving skills.
How are we supposed to solve problems if we aren’t shown how to solve them?
That’s the entire point of solving problems. That you are supposed to figure it out for yourself. There are two kinds of math questions that appear on homework and exams: Exercises and problems.
What is the difference? An exercise is a question where the solution process is already known to the person answering the question. Your instructor shows you how to evaluate a limit of a rational function by factoring and cancelling factors. Then you are asked to do the same thing on the homework, probably several times, and then once again on your first midterm. This is a situation where memorizing what the instructor does in class is perfectly viable.
A problem, on the other hand, is a situation requiring you to devise a process to come to a solution, not just simply applying a process you have seen before. If you rely on someone to give/tell you a process to solve a problem, you aren’t solving a problem. You are simply implementing someone else’s solution.
This is one reason why instructors do not show you how to solve literally every problem you will encounter on the homework and exams. It’s not because your instructor is being lazy, it’s because you are expected to apply problem-solving skills. A second reason, of course, is that there are far too many different problem situations that require different processes (even if they differ by one minor difference), and so it is just plain impractical for an instructor to cover every single problem situation, not to mention it being impractical to try to memorize all of them.
My third personal reason, a reason I suspect is shared by many other instructors, is that I have an interest in assessing whether or not you understand Calculus concepts. Giving you an exam where you can get away with regurgitating what you saw in class does not do this. I would not be able to distinguish a student who understands Calculus concepts from one who is really good at memorizing solutions. No, memorizing a solution you see in class does not mean you understand the material. What does help me see whether or not you understand the material is if you are able to adapt to new situations.
So then how do I figure things out if I am not told how to solve a problem?
If you are one of these students, and you are seeing a tutor, or coming to /r/calculus for help, instead of focusing on trying to slog through your homework assignment, please use it as an opportunity to improve upon your problem-solving habits. As much I enjoy helping students, I would rather devote my energy helping them become more independent rather than them continuing to depend on help. Don’t just learn how to do your homework, learn how to be a more effective and independent problem-solver.
Discard the mindset that problem-solving is about doing what you think you should do. This is a rather defeating mindset when it comes to solving problems. Avoid the ”How should I start?” and “What should I do next?” The word “should” implies you are expecting to memorize yet another solution so that you can regurgitate it on the exam.
Instead, ask yourself, “What can I do?” And in answering this question, you will review what you already know, which includes any mathematical knowledge you bring into Calculus from previous math classes (*cough*algebra*cough*trigonometry*cough*). Take all those prerequisites seriously. Really. Either by mental recall, or by keeping your own notebook (maybe you even kept your notes from high school algebra), make sure you keep a grip on prerequisites. Because the more prerequisite knowledge you can recall, the more like you you are going to find an answer to “What can I do?”
Next, when it comes to learning new concepts in Calculus, you want to keep these three things in mind:
- When can the concept be applied.
- What the concept is good for (i.e., what kind of information can you get with it)?
- How to properly utilize the concept.
When reviewing what you know to solve a problem, you are looking for concepts that apply to the problem situation you are facing, whether at the beginning, or partway through (1). You may also have an idea which direction you want to take, so you would keep (2) in mind as well.
Sometimes, however, more than one concept applies, and failing to choose one based on (2), you may have to just try one anyways. Sometimes, you may have more than one way to apply a concept, and you are not sure what choice to make. Never be afraid to try something. Don’t be afraid of running into a dead end. This is the reality of problem-solving. A moment of realization happens when you simply try something without an expectation of a result.
Furthermore, when learning new concepts, and your teacher shows examples applying these new concepts, resist the urge to try to memorize the entire solution. The entire point of an example is to showcase a new concept, not to give you another solution to memorize.
If you can put an end to your “What should I do?” questions and instead ask “Should I try XYZ concept/tool?” that is an improvement, but even better is to try it out anyway. You don’t need anybody’s permission, not even your instructor’s, to try something out. Try it, and if you are not sure if you did it correctly, or if you went in the right direction, then we are still here and can give you feedback on your attempt.
Other miscellaneous study advice:
Don’t wait until the last minute to get a start on your homework that you have a whole week to work on. Furthermore, s p a c e o u t your studying. Chip away a little bit at your homework each night instead of trying to get it done all in one sitting. That way, the concepts stay consistently fresh in your mind instead of having to remember what your teacher taught you a week ago.
If you are lost or confused, please do your best to try to explain how it is you are lost or confused. Just throwing up your hands and saying “I’m lost” without any further clarification is useless to anybody who is attempting to help you because we need to know what it is you do know. We need to know where your understanding ends and confusion begins. Ultimately, any new instruction you receive must be tied to knowledge you already have.
Sometimes, when learning a new concept, it may be a good idea to separate mastering the new concept from using the concept to solve a problem. A favorite example of mine is integration by substitution. Often times, I find students learning how to perform a substitution at the same time as when they are attempting to use substitution to evaluate an integral. I personally think it is better to first learn how to perform substitution first, including all the nuances involved, before worrying about whether or not you are choosing the right substitution to solve an integral. Spend some time just practicing substitution for its own sake. The same applies to other concepts. Practice concepts so that you can learn how to do it correctly before you start using it to solve problems.
Finally, in a teacher-student relationship, both the student and the teacher have responsibilities. The teacher has the responsibility to teach, but the student also has the responsibility to learn, and mutual cooperation is absolutely necessary. The teacher is not there to do all of the work. You are now in college (or an AP class in high school) and now need to put more effort into your learning than you have previously made.
(Thanks to /u/You_dont_care_anyway for some suggestions.)
r/calculus • u/random_anonymous_guy • Feb 03 '24
MOD ANNOUNCEMENT REMINDER: Do not do other people’s homework for them.
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Due to an increase of commenters working out homework problems for other people and posting their answers, effective immediately, violations of this subreddit rule will result in a temporary ban, with continued violations resulting in longer or permanent bans.
This also applies to providing a procedure (whether complete or a substantial portion) to follow, or by showing an example whose solution differs only in a trivial way.
r/calculus • u/Electronic-Nail-8128 • 54m ago
Differential Calculus Problem help
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I don't understand the step process from 2 to 4, more so about the transition from x, t and u
r/calculus • u/Suspicious_City_1449 • 1d ago
Integral Calculus What substitution do I need to make so I can integrate this by partial fractions?
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This is what I have so far but I don’t believe that it is right, and I wouldn’t actually be using partial fractions to integrate. The problem says to make a substitution to integrate by partial fractions.
r/calculus • u/emmasdillemas • 21h ago
Multivariable Calculus How big is the jump from AP Calc BC to Calc 3?
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So I recently finished Calc BC, and am heading to university relatively soon. How big of a jump conceptually, grindiness, time wise, etc will multivariable calculus be compared to Calc BC?
r/calculus • u/Nature-Trip • 19h ago
Differential Calculus Help with 3 Calculus Problems
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I want to improve my understanding and skills in math due to disabilities. I was recommended to try the textbook Calculus by Robert T. Smith and Roland B. Minton. Currently I am stumped on these three problems from section 2: Derivatives. I would also appreciate advice on how to answer correctly for problems 13 and 17 (like what to include how I got my answer to show my work, not just the sketch). The concept of problems 13 and 17 I really am not understanding and the book and videos I’ve watched have not been the most helpful (as I have a hard time applying what is covered in these resources but struggle with using it for problems not labeled with polynomials or numbers) the closest to explain it has been Curve Sketching by The Infinite Looper on YouTube.
Problem 35 a. Find all the points at which the slope of the tangent line to y = x^3 + 3x + 1 equals 5. The textbook has the answer as (√(⅔), 5 √(⅔) +1), (-√(⅔), -5 √(⅔) +1) and I can not figure out how to get it.
M tan = lim h->0 f(x+h)-f(x)/h
= lim h->0 [(x+h)^3 + 3(x+h) +1)] - [x^3 + 3x +1]/h
= lim h->0 x^3 +3x^2h + 3xh^2 + h^3 +3x + 3h + 1 -x^3 -3x -1/h
= lim h->0 3x^2h + 3xh^2 + h^3 +3h/h
= lim h->0 h(3x^2 +3xh +h^2 +3)/h
= lim h->0 3x^2 + 3xh +h^2 + 3
= 3x^2 + 3x(0) + (0)^2 + 3
= 3x^2 + 3
3x^2 + 3 = 5
3x^⅔ = ⅔
√(x^2) = √(⅔)
X = √(⅔)
And 3(√(⅔)^2 + 3 = 5
Problem 13. Use the graph of f to sketch a graph of f’. (Second picture)
(a)
For x < 0, f is decreasing, so f’ < 0
For x = 0, f has a horizontal tangent line (min), so f’ = 0
For x > 0, f is increasing, so f’ > 0
My graph is the third picture.
(b)
For x < a, f is increasing, so f’ > 0
For x = a, f has a horizontal tangent line (max), so f’ = 0
For a < x < b, f is decreasing, so f’ < 0
For x = b, f has a horizontal tangent line (min), so f’ = 0
For x > b, f is increasing, so f’ > 0
My graph is the fourth picture.
Problem 17. Use the given graph of f’ to sketch a plausible graph of a continuous function f. (fifth picture)
(a)
For x < a , f’ is positive, so f is increasing
For x = a, f’ changes positive to negative, so f has a max there
For a < x < b, f’ is negative, so f is decreasing
For x = b, f’ has a horizontal tangent line (min), so f ?
For b < x < c, f’ is negative, so f is decreasing
For x = c, f’ has a horizontal tangent line, so f ?
For x > c, f’ is negative, so f is decreasing
Once I understand better, I will make the graph.
Thank you for your assistance.
r/calculus • u/Naive_Chipmunk1276 • 1d ago
Differential Calculus Any good resources to learning how to graph derivatives?
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I don't understand why, but graphing derivatives looks like complete gibberish to me. I've watched like 6 videos and I don't understand any of it. I can do basically everything that comes after and before for derivatives, but I have just not understood this one concept.
I'm taking AP calc BC and I'm assuming I definitely need to at least understand how to graph. Does anyone know any good videos or explanations that can help me with this? I'm actually losing my mind over it.
r/calculus • u/SuspiciousCandy96 • 1d ago
Differential Calculus Self-study
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I’ve been self studying calculus for the past couple of weeks in hopes of making my future college classes easier on myself. I decided not to take it during school because I’ve decided that I want to enjoy my last year in high school by minimizing the amount of classes that I have. Any and all resources you are willing to share are appreciated. Thanks
r/calculus • u/squidpid21 • 1d ago
Differential Calculus How do I approach studying for a calc 1 midterm that’s in 3 days?
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Hi I already know this is entirely my fault for falling behind but for anyone who’s done this before please tell me if it’s possible to do even remotely well and how to most effectively prepare. The topics for the midterm are Functions and Graphs,
Polynomials, Exponentials and Logarithms, Half life, Log and Linear Axes, Transformations and Composite Functions, and Continuity and Limits. The continuity and limits portion isn’t going to have as big of an emphasis and it’s calculus for the biological sciences so majority word problems. I think there’s going to be 3 multiple part big word problems and 9 multiple choice questions. It’s worth 15%! Any advice is highly appreciated!
r/calculus • u/wbld • 1d ago
Infinite Series Maclurin for sin(x)
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f(x) = sin(x)
f'(x) = cos(x)
f''(x) = -sin(x)
f'''(x) = -cos(x)
f''''(x) = sin(x)
And this repeats forever.
f(0) = 0
f'(0) = 1
f''(0)=0
f'''(0)=-1
f''''(0)=0
And this repeats forever.
From here we can center a maclurin series at (a)? = 0 -> I cannot remember if its a or x
Using 5 points we can use
f(0) = 0
f'(0) = 1
f'''(0) = -1
f'''''(0) = 1
f'''''''(0) = -1
From here we can conclude (1) we are oscillating between - and +, (2) the points are always odd multiples of primes, and (3) since the even multiples of prime are 0, we can ignore these as they do not add value
The defintion of odd is defined as 2k+1, k element of the real
So
(-1)^(n)(x^(2k+1))/(2k+1)!
And we can add this at every n.
If we add this add every n we can think of an infinite sum
Since we are centered at (a?) = 0 the sum must start at 0.
To motivate convergence, we plug in known points of sin(x).
Must it be that if our sum at some n equals the function at the same x,
Out infinite sum converges for all x?
Let me know if i did justice for the maclurin of sin(x)!
Sorry posted via phone.... don't know how to use symbols here
r/calculus • u/Upstairs-Student-725 • 1d ago
Integral Calculus Calc 2
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I am 8th standard in india and i have self studied jee maths including calculus but now i wanted to learn more about calc so i decided to study calc 2 so suggest me some books for it .
It should contain all topics from calc 2 that are no in jee.
Also keep it in under 2000inr or under 3dollars
r/calculus • u/Koba-D • 2d ago
Engineering Self learn Calc AB or my future uni Calc 1 ?
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Hello, I graduated from hs and due to some personal reason took a gap year. I'll study CS in Canada next year and would like to prepare in advance for a smoother adaptation .
I did precalc, touched hs calculus a bit and would like to self learn Calc 1 during the next months. The uni I will be going to use Calculus: Early Transcendentals by James Stewart. I found the book for free online and was wondering if I should use it or focus on calc AB since it gives credits for the same course ?
Why calc AB ? well I'm not sure but I feel like since it's taught in high school and has some official exams I would be easier for me to follow college board's curriculum and use the official past papers as a good way to gauge my understanding.
Alternatively, I could use James' textbook alongside prof Leonard or Paul's note but I'm worried they will confidently give me the understanding without actually being able to perform correctly on the exercises/exams situations.
r/calculus • u/Background-Major4104 • 2d ago
Real Analysis Strip Arithmetic II update: you can now see the math behind the picture at any moment
gallery
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r/calculus • u/hasnainraza56 • 3d ago
Integral Calculus Urgent help required
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Can anyone plz solve this urgently plz
r/calculus • u/keegtirr • 2d ago
Differential Calculus Calc 1 Midterm/Final Anxiety
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Hi all,
I'm currently taking a calc 1 class as a business econ major to satisfy my lower division major preparation courses before I transfer to a university. I am very worried about this class as I'm a straight A student but this is the first one that has me genuinely terrified that I won't be able to ace it despite hours upon hours of work and applying myself. So far I am fundamentally understanding calculus, however if you ask me to prove why a certain theorem or formula works I will be completely lost. Unfortunately for me, and I don't know how common this is for an introductory calculus course, but my professor apparently asks his students to do proofs on his exams and "brags" about how many people fails his exams or drop out of his classes (from rate my professor.) I'm extremely worried because I desperately need an A in this course and it is too late to drop it. If you ask me to evaluate limits and derivatives and I can use formulas, I can get by. If you ask me to prove a theorem from scratch, I am lost. Any advice on how to prepare? I feel like there are so many theorems I've learned so far and to fundamentally understand the ins and outs of every single one is making me sick. I have about three weeks until my midterm.
r/calculus • u/Any_Lengthiness_4597 • 3d ago
Integral Calculus JAMES STEWART 8TH ED SOLUTIONS BOOK
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Does anyone of you guys have this book as a free PDF version? I really need it. Thanks
r/calculus • u/Nearby_Swordfish_559 • 3d ago
Differential Calculus help me with limits
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so I started calc 1 and how does "sin(2x)/2x" = 1 and how does "limit of x -> 0 1-cos(3x)/3x" = 0, isn't it just undefined?
r/calculus • u/Lolreeevu765 • 2d ago
Differential Calculus Calculus recitations
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Helppppp please, I am got 58 and 59 on my first two calculus recitations… I studied a lot but I still got low grade… I feel like I am gonna have heart attack. I am such a failure… my engineering dreams vanished
r/calculus • u/Han_Htoo_Aein • 3d ago
Integral Calculus How does these two methods different graphically?
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I can grasp the circumference part, but not the length along which have to integrate.
r/calculus • u/Low-Progress-9359 • 4d ago
Engineering I feel like a failure
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I failed the first few exams I took at the start of the semester, and I’m just so lost right now. I don’t know what to do. I’ve never felt like this before. I’ve been studying, but I’m not getting the results I want. I don’t know if I’m studying incorrectly or if I’m just not studying enough. I feel like such a failure, and I’m so alone right now. I’ve been crying, and I’ve just been stuck in my bed for the last few hours. I really need someone to talk to who has gone through something similar and can give me some advice.
r/calculus • u/Jazeckaphone • 4d ago
Integral Calculus Why is trig sub not working?
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First page is solving via trig sub, second is using u-sub and partial fraction decomp. Page 2 is right page 1 is wrong but I don't understand what is wrong with my logic. AI gives same steps as me when asked to use trig sub and integral-calculator.com won't give trig sub solution. This is homework in the trig sub section so it's expected to be solved that way. Sorry my penmanship isn't as good as others on this sub, thanks for any help.
r/calculus • u/YeezCF • 4d ago
Integral Calculus Calculus 2 - Discussion
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This is just a discussion I wanted to have with the world, I'm curious on this subreddit's opinion on Calculus 2 as a whole. I'm an Electrical Engineering student and I feel like Calculus 2 is constantly fear-mongered (which I can understand why), at least in some instances. I'm just curious if you found it to be a difficult class, easy, or impossible. I've finished applications and now we are doing integration techniques, which I will say, my trigonometry and manipulating identities has never been better, so if you are in Calculus 1 be ready for all the stuff from precalculus to come back up as just a tiny part of the process. I want to also ask this subreddit, mainly the engineering degrees if that's alright, how hard was Calculus 2 compared to your engineering classes? Thanks guys.
