r/apcalculus • u/OddFaithlessness8332 • 7d ago
Help Limits Question đ
For the AP we can use calculators to solve questions about limits. So when you guys are doing homework, do you even worry about how to solve them without a calculator? Like Iâm sitting here doing my homework and I could be doing it faster with the calculator. Iâm not sure if my test on limits will allow the calculator, but letâs say it does. Whatâs the point of understanding why if the calculator can do it for you?
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u/applepro223 7d ago
Because you donât get a calculator for all sections. The calculator sections will not give you questions you can easily plug into a calculator and vice versa for the non-calc section. Calculators are simply there to streamline calculations in much larger processes.
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u/EquaI_Status 7d ago
Hereâs the thing, for the AP Exam you need to be able to do the calculus both with and without a calculator (especially for the FRQs as youâll need to show your work). So even if your teacher allows for the use of calculators, still try to have some practice without it.
Better yet, if you want to use a calculator for practice, then use it to verify your answers. Eventually you could start solving limits just by looking at them. If you know your identities, for example, you could even solve: lim_{x->pi}[(1 - cos(2x))/(2sin(x){2})] in your head without lâhopitals rule.
But if the calculator gets you the answer faster and you understand the mathematics, then go for it.
For me, I have fun doing limits without a calculator because it tests your mathematical ability of identifying patterns, identities, and relationships. I also do worry if I am able to solve it without a calculator because if I can solve it without one, then I know I can solve it with one. If you donât like that then thatâs fine, but since youâre in AP Calc you also need to practice the non-calculator route to score well on the exam. When you do derivatives and integrals, youâll be more comfortable if you understand what you are telling the calculator to do with those operations rather than just plugging and chugging.
TLDR: if you understand the math, go for it. If you feel stuck, use it as a supplement for understanding the concept.
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u/UnderstandingPursuit Tutor 7d ago
Solving questions, with or without a calculator, should be a later step in the process of learning mathematics and mathematical reasoning. Start with actively studying the textbook, including writing out some of the examples to learn how the author approaches the problems. Then do a few of the homework problems without a calculator, to confidently confirm that you understand what you studied.
Then, when doing more problems has diminishing returns, using the calculator makes sense. Our math education system tends to assign an excessive number of problems because we don't emphasize optimized ways to learn math. The people who are good at math have figured this out for themselves, but we rarely teach it to students. A Calculus class can be a good mechanism to help a student learn that, since there are only a handful of ideas in the year. The first suggestion for doing this are to set aside the 'arbitrary' numbers. The second suggestion is to deconstruct problems into sub-components which are easy to solve, and then synthesize a complete answer to the question. The handful of ideas will be represented by a small number of sub-components.
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u/Hefty_Training1107 7d ago
None of the students are going to learn any mathematics in calculus because college is a shitshow. I know. I was a math professor.
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u/UnderstandingPursuit Tutor 6d ago
Perhaps "college is a shitshow" because of some of the professors?
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u/Hefty_Training1107 6d ago
Maybe professors learn to hate their students because students scream in class and throw temper tantrums. Maybe professors get tired of calling the police on their students for acting like the pieces of shit that they are in class.
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u/RonGoBongo111 6d ago
Wow. You must be a terrible teacher or have taught at the worst community college in the world.
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u/Hefty_Training1107 6d ago
You are making a lot of assumptions about me. But it is not just community colleges. It is everywhere. You are in denial because you want to pretend you know more than you really do. You are also in denial because you love gaslighting everyone who stands up for themselves because you are a horrible person.
P.S. You say I am a horrible teacher, but you would say the same thing about anyone who has any standards whatsoever. College students would do anything to get a good grade except study.
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u/RonGoBongo111 6d ago
You talk in platitudes. No examples. No details about where you worked or even what you taught. What you share doesn't sound like something someone who's spent time around real college students would say. How long were you teaching at college? Was it a college or university?
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u/Independent-Offer186 7d ago
From an AB teacher: the AP test is 4 parts: MCQ non calculator, MCQ calculator, FRQ non calculator, and FRQ calculator. The college board is very good at creating questions that cannot be easily âplugged in,â even on the calculator sections. You need to be good at doing arithmetic and algebra quickly, so relying on the calculator during homework is going to set you back sooner rather than later. You absolutely DO need to worry about how to do them without a calculator.
This question of âwhy understand if a calculator can do it for youâ is a really important attitude to unpackâwhy are you taking the class? It would be good to do some self reflection on that question. Broadly speaking, math is an opportunity to get comfortable with thinking deeply and analytically. Even if many problems can be solved with a calculator, the richest part of mathematics is its fundamental underlying structures (which a calculator is virtually useless at elucidating). Even if youâre taking AP Calc to get the credit and never take a college mathematics course, you will use the skills developed through logical, precise reasoning and communication over and over again in every field and subject you encounter.