kingpomba's noobtacular question-a-rama thread

[slothpomba]

Hey guys, i figure i better make a thread because I'm probably going to start using it a lot. I'm not exactly *fantastic* at math so i seriously appreciate all the help (my aim is to get a raw 25, nothing super high). I also go to a tutor for methods and he gave me some homework to do - i scanned it - ill type my questions however.

I guess my first question would be this one:

4
Evaluate:
(B)

I tried subbing in x=1 and it ended up undefined, this isnt the answer. I remember the tutor saying you had to do something to it but i forgot exactly what..

Thanks for all the help, kingpomba

[Lighties]

You have to simply it first.

So factorise , then cancel with denominator, and then sub x=1 in. (:

*If you sub a number in and it ends up undefined, you usually have to simply the term first.

[brightsky]

You cannot sub 1 in, hence the limit is in indeterminate form 0/0, so you need to apply Bernoulli's rule through using derivatives to solve the limit as f'(x)/g'(x) exists:







Now you can substitute x = 1 in and you'll get:

[brightsky]

Or yes, an easier way would be:



Hence,

[Lighties]

For your first solution, is that part of the Methods course? Because I don't remember learning that at all.

[slothpomba]

How about something like this:
Derive:


Heres what i got:

(collect like terms)
(derive)


The answer however is

[GerrySly]

How about something like this:
Derive:


Heres what i got:

(collect like terms)
(derive)


The answer however is

I believe you've either read it incorrectly or the book is wrong

[Lighties]

End of your first line, it's supposed to be +1. But doesn't matter once you start deriving.

Your deriving is wrong in the third line.

, once derived, goes to . Also, the -2 is supposed to be -2x. Fix that and then continue. (: Also, you could've simplified further with the x^2 terms. (:

I just did it quickly in my head and the answer doesn't seem to be ... or my brain might just be dead.

[TrueTears]

You cannot sub 1 in, hence the limit is in indeterminate form 0/0, so you need to apply Bernoulli's rule through using derivatives to solve the limit as f'(x)/g'(x) exists:







Now you can substitute x = 1 in and you'll get:

L'hopitals theorem to be precise.

See it in use here: http://vcenotes.com/forum/index.php/topic,12907.0.html

[superflya]

yea gerrys got it
ur expansion is wrong first off.

[TrueTears]

Notice another application of l'hopitals theorem is when you have

[brightsky]

Let amd

Hence and

By the product rule,



Even my CAS says this is right! :p

[slothpomba]

From Essential Mathematical Methods 3 & 4 CAS (Yeah i know these are easy but im terrible at math, which is why im here )

(Questions in red)
Exercise 1B:

(4) Consider the function
     (a) Find (already done this)
      
 SOLVED  (b) State the range of g (this im not really sure how to do, couldnt the range be from infinity...to infinity? depending what you sub in)[/s]


 SOLVED (5)  Let   &  

     (c) Express the following in terms of x

         (ii) f(x-2)
          -2x
          =2x^2-8+(-8x)
          
          (book)  Answer  is:

          (iv) g(x+2)
          
          
          
          


     (6) Consider the function . Find:
      SOLVED      (a)The image of 3
          SOLVED    (b)The pre image of 11
          SOLVED   (c){}[/s]

          (dont really understand any of these, bad text book examples, any help with even only 1 questions would be greatly appreciated.)

[coletrain]

From Essential Mathematical Methods 3 & 4 CAS (Yeah i know these are easy but im terrible at math, which is why im here )

dw bro, your not the only one

[Stroodle]

For your first question you can either find where the derivative equals zero, graph the function, or reason that any value of x will be squared (making it positive), therefore the lowest value of the function will be -2 where x=0, and the highest value will be infinity: