Math Is Fun Forum

Thank you so much Cushydom.

This works incredibly well. Can I ask how you worked it out?

Thanks a bundle bossk172. I was indeed looking for a quadratic. Do you mind me asking how you came up with it?

luca-deltodesco, it appears you do have the correct answer, but I really don't understand your method. I fear you may have used techniques I haven't yet been taught, and hence, I doubt they'll need to be implemented in the exam. However, thanks for your input and well done for getting the correct answer.

Stardust, yep, that's it! I understand that, it's one of those answers you think, how the hell didn't I get that!? Haha. Fantastic! Thank you so much. And no, my M1 exam is on Tuesday! Do you get an extra day!?

Yeah, I see where I've went wrong. I began to plug in limits when it was all relative to dx, forgot to do the whole dx/dθ=sec²θ and rearrange that to replace dx. Thanks a bunch guys, again. You've been a fantastic help.

I have the answer, if it's of help:

Although it's smack bang in front of me, I still can't understand it, so could anyone work it through for me? Cheers, Tredici.

Oops, sorry for spam.

Woah, a fair few responses to this thread. I've been thinking about this factorial business, and I'm wondering if a different way of thinking may make understanding why 0! is considered to equal 1 that little bit easier.

I've considered all of the above mentioned formulae during pondering this, but I fail to see how they can be used as proof. Formulae like the permutations and factorial formula where derived with knowledge that any real number less than zero cannot be applied, even fractions/decimals >0,<1 in the Gamma function. In this instance, the likes of Leonhard Euler forever disregarding the application and resultation of negative numbers as 'acceptable' seem sensible mathematicians.

Using n!/(n-1)!=n does seem sensible at first thought, but by accepting the continuation of the rule such that 1= (1)!/(0)!, you must consider the resultant of further applications, like 0= (0)!/(-1)!, and -10= (-10)!/(-11)!, and that's when it becomes slightly less reasonable.

I'm sure we're all in agreeance in respect to a factorial being the product of all positive
integers from 1 to a given number. With this definition strictly in mind, 0 can not be applied as it's distance from 1 in a 1,2,3.. sequence is restricted by the realms of negative infinity, using the term 'negative infinity' very loosely. This is all obviously ignoring a vector like existance, where 0 is -1 from 1, which cannot be used here.

If we think more application as opposed to the confinements of laws, rules and constraining equalities maybe it begins to make sense. For example, what exactly is factorial? Well, factorial is just a simpler version of the permutations forumla, where n = r. Therefore, we're given all the different arrangements of n objects which are taken n at a time.

With this in mind, Let's imagine I've just spent a beautiful day by the lake side and have caught myself two wonderfully sized fish, they're so large in fact I'm going to name them Lance and Roy. Now, how should they sit on my plate when I have them for dinner? Well, I can have Roy, Lance or Lance, Roy? (2!=2). Hmmm, decisions, decisions.

Now, the day after, the clouds swell and stain black, and a powerful rainstorm hits the villiage. Being such a poor man, I rely entirely on fish, and must go out, once again, and try to catch some. But nope, not today. I get home, sling my rod to the floor, reach for the cupboard, grab a plate and stare, green with envy, nostalgic with the thought of yesterday's plentiful supper in mind. With the painful sound of my stomach rumbling and the food depriving rain attacking my straw roof, I think, how many times can 0 fish sit on my plate, and that's only 1 way, with no fish whatsoever. .:. 0! = 1

I realise I've just wasted about 5 minutes of your lives, but oh well, atleast I'm now entirely sure you've all gotten my point .

3? Out of 3? Correct? .

Lmao, that's crazy, wouldn't of done it without you guys.

Let's suppose the last question was:

f(x) = 3e^x - ½ ln (x - 2) as oppose to f(x) = 3e^x - ½ ln x - 2

Would it then be..

(3e^x)' = 3e^x

(½ ln x - 2)' =  is that just, ½ 1/(x-2)? or simplified 1/(2x-4)

∴  ƒ'(x) = 3e^x - 1/(2x-4). Not quite so sure on that one, to be honest.

Oh guys I've just noticed, I haven't made myself too clear; I've written a x sin(x) when I meant more along the lines of (a)times[sin(x)]. How would that be differenciated?

Edit: Don't worry, I got it . Silly me.