I mean just plug in the numbers and you'll get your answer. right?
2006-12-22 09:55:40 · 13 answers · asked by Nicolas M 1 in Science & Mathematics ➔ Mathematics
With calculus? No. You kinda need to understand what you're doing even to plug it in.
2006-12-22 09:58:28 · answer #1 · answered by eri 7 · 3⤊ 0⤋
On top of what the others have already mentioned, there's also the fact that sometimes, even when you plug in the correct equations and the correct numbers, you WON'T get the right answer. Consider the following two graphs:
http://img206.imageshack.us/img206/1730/graph1nv6.png
http://img205.imageshack.us/img205/7366/graph2gw6.png
Both of these are graphs of the same polynomial over the same domain. But you'd never get that from just the image, because one of these graphs is horribly, horribly wrong. This is not because the polynomial was entered incorrectly, but because one of the graphs was computed using a method that while correct in theory, has horrible numerical stability. Finding numerically stable algorithms for computation is a field all by itself (look up numerical analysis, if you're interested), but even without knowing a darn thing about numerical analysis, someone who understood the behavior of polynomials would instantly know that the second graph is horribly, horribly wrong. Whereas someone who just plugs and chugs would probably announce that they've discovered a polynomial of degree 7 with several thousand roots. That's one of the reasons why, even if you have access to a full-featured computer algebra system, you still have to know the material, so that you can tell when what the CAS is telling you is incorrect.
2006-12-22 20:06:45 · answer #2 · answered by Pascal 7 · 0⤊ 0⤋
No. Even the best of calculators cannot calculate some integrals; it requires human logic. You have to know calculus to know which buttons to press and to determine whether the answer seems logical. You should do the problems by hand and then check them with your calculator. Plus, only a select few calculators can calculate a derivative; a TI-83 (the most common graphing calculator) cannot. If one were to simply plug everything into the calculator, he would not know why it works or how to do it. In the real world however, you will most likely not have to calculate problems on your own without technology, unless you are teaching it.
2006-12-22 18:51:10 · answer #3 · answered by j 4 · 1⤊ 0⤋
One can say the same thing about a lot of things.
Why learn to read when you can have people read for you?
Why learn to the do the laundry when you can have people do it for you?
With that answer aside, the concepts of Calculus can't be done using a regular calculator. It's the logic involved that counts. One thing Calculus does is teach us to think logically and improve our abiliity to deduce and reason.
With that said, pre-Calculus actually does allow calculators on tests, and if it's all about plugging in your numbers and getting your answer, then everybody should get an A+, right? Because they don't, it's more than "plugging in numbers".
2006-12-22 18:02:16 · answer #4 · answered by Puggy 7 · 3⤊ 0⤋
Most of the problems on first semester calculus tests don't even require a calculator. With most mathematics algebra and above, most of the work is spent figuring out equations which tell you which numbers to put into a calculator. Or in other words, your calculator won't give you the right answer if you don't know which numbers to put in and what to tell the calculator (or computer) to do with them.
2006-12-22 18:05:56 · answer #5 · answered by Faeldaz M 4 · 2⤊ 0⤋
There are only a few calculators out there that will solve calculus problems for you, and even with those, you have to understand the calculus and know how to enter the problem to get the calculator to give you the answer.
2006-12-22 18:03:16 · answer #6 · answered by rinkrat 4 · 3⤊ 0⤋
A calculator can be lost or stolen. The batteries can go dead. The keys can break down and cease to function. The display can fail, in part, or in toto. If it is solar powered, the solar cells can fail.
On top of all that, how do you know when you've pressed the right keys? When you solve a problem using calculus, you've learned something. When you punch a bunch of keys on a calculator, you haven't.
2006-12-22 18:08:35 · answer #7 · answered by Helmut 7 · 3⤊ 1⤋
Fraid not.
You need calculus to know which buttons to press. The calculator does come in handy at the end though.
2006-12-22 18:18:41 · answer #8 · answered by crazy_tentacle 3 · 1⤊ 0⤋
You need to learn English first if you want to read a dictionary.
2006-12-26 01:01:33 · answer #9 · answered by _anonymous_ 4 · 0⤊ 0⤋
Why learn English when you have a dictionary?
Why learn how to walk when you have a car?
Why learn science when nobody will listen to it?
2006-12-22 17:57:26 · answer #10 · answered by Anonymous · 3⤊ 0⤋