Limits suck

Samith · 2003-10-16T11:37:49

Lets say we have the function f(x) = x2 Then how do we calculate a tangent line at say point 4, using limits? If a tangent line is lim(b->a, (f(b)-f(a))/(b-a)) (sorry for the messy parentheses) wouldn''t that juse equal 0/0? Or.....am I missing something with the calculation of limits?

Math and Physics Programming

Started by Samith October 15, 2003 08:22 PM

18 comments, last by Samith 20 years, 6 months ago

Nervo

344

October 15, 2003 09:18 PM

quote:Original post by ZealousElixir
quote:Original post by Nervo
Yes, I do agree with you. But he asked for it!

No, he asked (1) how to calculate a tangent via limits and (2) what method experienced people would use. The second question came as a response to the lame method of doing it manually. It would seem that he wants the mathematical basis for calculating the derivative. After all, the power rule is just a shortcut to a derivative.
quote:Original post by Nervo
He can also research on google for "proof+derivative" to see if it makes sense to him.

No, and that''s exactly the point. It won''t make sense until he practices the fundamental methods on his own, or is taught the steps of the proper way. Of course the mechanics are easy to implement, but only when people hand you the formula, which doesn''t teach anyone anything.

Not flaming, I just have serious issues with circumventing the normal modes of understanding how to problem-solve.

Well ZealousElixir, I''m not about to try and write out proofs and methods for differentiating for Samith. I don''t see any problem in showing him the mechanics of it if he doesn''t need it for school or something critical. I think you need to calm down.

Well, R2D22U2..

Anonymous

October 15, 2003 09:28 PM

the derivative only solves for slope, you still have to solve the equation for mx, which is 8 * 4. So the equation for the tangent line is found by doing:

16 = 32 + b
b = 16 - 32 = -16

so the equation in point slope form of the line tangent to the curve y = x^2 is y = 8x - 16

shadow12345

100

October 15, 2003 09:28 PM

the derivative only solves for slope, you still have to solve the equation for b taking into account *mx* (slope multiplied by time) which is 8 * 4. So the equation for the tangent line is found by doing:

16 = 32 + b
b = 16 - 32 = -16

so the equation in point slope form of the line tangent to the curve y = x^2 is y = 8x - 16

EDIT: and I got the 16 because in the original equation 4^2 equals 16 (that is the value of the single point you want to touch)

[edited by - Shadow12345 on October 15, 2003 10:32:47 PM]

[edited by - Shadow12345 on October 15, 2003 10:34:31 PM]

Why don't alcoholics make good calculus teachers?Because they don't know their limits!Oh come on, Newton wasn't THAT smart...

Samith

2,465

Author

October 15, 2003 09:43 PM

Hmm, about that n*xn-1 rule, while I haven''t found a proof, I worked it out for f(x) = x3

I don''t see how you would prove it, but I see how it works. It''s really simple, as it can be derived from simple algebra. I don''t know about the proof though, I''m assuming it''s probably a bit over my head. But, whatever, thanks for all the help

zealouselixir

256

October 15, 2003 09:44 PM

quote:Original post by Nervo
Well ZealousElixir, I''m not about to try and write out proofs and methods for differentiating for Samith. I don''t see any problem in showing him the mechanics of it if he doesn''t need it for school or something critical. I think you need to calm down.

Uhoh, we''ve devolved into addressing by name and telling the other person to become less anally-retentive. For the love of all things good, I''ll concede. You''re right after all - if it''s not for school, what''s the point of understanding how it works?

[twitter]warrenm[/twitter]

Nervo

344

October 15, 2003 09:46 PM

quote:Original post by ZealousElixir
quote:Original post by Nervo
Well ZealousElixir, I'm not about to try and write out proofs and methods for differentiating for Samith. I don't see any problem in showing him the mechanics of it if he doesn't need it for school or something critical. I think you need to calm down.

Uhoh, we've devolved into addressing by name and telling the other person to become less anally-retentive. For the love of all things good, I'll concede. You're right after all - if it's not for school, what's the point of understanding how it works?

You appear unable to critically read. I'm not saying there is no point to understanding how it works, yet I am saying that it is not critical for him to understand it at his current position in math, but resources are available on the net for him to give it a try.

[edited by - nervo on October 15, 2003 10:49:46 PM]

Well, R2D22U2..

GaulerTheGoat

122

October 15, 2003 09:56 PM

quote:Original post by Samith
I always thought you were supposed to calculate limits by substituting in the variable with the constant number it''s approaching.

When you can "plug in the value" is refered to as continuity. Since this sounds like a beginning calc class, I''m sure you''ll cover that soon enough

The idea is loosely, if the graph can be drawn without picking up your pen at the point you are taking the limit, then you can plug the x value in and evaluate. If plugging in creates an expression that is undefined (like 0/0), then you need to try and factor something probably.

This probably doesn''t help you with your original question but just keep it in mind: sometimes you can plug in and sometimes you can''t (in calc 1, the times you can''t are usually ridiculously overt

)

Hope that helps

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Samith

2,465

Author

October 15, 2003 09:59 PM

GaulerTheGoat: I''m not in calculus yet, I''m still in FST (Function, Stats, Trig, for those that don''t go to my school or know what this is or something....) I''m just doing this stuff for fun.

GaulerTheGoat

122

October 15, 2003 10:10 PM

quote:Original post by Samith
Hmm, about that n*xn-1 rule, while I haven''t found a proof, I worked it out for f(x) = x3

I don''t see how you would prove it, but I see how it works. It''s really simple, as it can be derived from simple algebra. I don''t know about the proof though, I''m assuming it''s probably a bit over my head. But, whatever, thanks for all the help

True.

You have discovered a theorem of calculus. You should be proud. You have joined the ranks of Newton and Leibniz

If your book is any good, it probably has a big list of these things on the front or back cover. The proof is probably in the section about derivatives.

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grhodes_at_work

1,385

October 16, 2003 11:37 AM

This reeks of homework, and I'm closing the thread. Please review the forum FAQ (see link below) and in the future at least follow the guidelines when posting anything that is even close to a homework question.

The FAQ also has links to places where homework is the norm.

Forum FAQ

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

[edited by - grhodes_at_work on October 16, 2003 12:37:49 PM]

Graham Rhodes Moderator, Math & Physics forum @ gamedev.net

Limits suck

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