The Rule for Finding Limits of Difference of Powers: (a^n - b^n)

[shawshank]

limit of x --> 1

(x^1000 - 1 ) / (x-1)

 

[sutupidmath]

what have you done so far? show your work before someone here gives you any hints!

 

[shawshank]

lim of x ---> 1

(x^1000)(x+1)/(x^2-1)

hahah, lol just kidding.

seriously, have no clue where to start.

 

[sutupidmath]

ok, then let's do this before i get out of here:
well i am going to try to give u a hint
$$a^{n}-b^{n}=(a-b)(a^{n-1}+a^{n-2}b+a^{n-3}b^{2}+a^{n-4}b^{3}+...+a^{2}b^{n-3}+ab^{n-2}+b^{n-1})$$, in your problem a=x, b=1 , and n=1000, also remember that 1=1^1000, or any other real power.


i hope this will do u any good!

 

[shawshank]

thanks i got it, it's 1000. What is the rule called the (a^n - b^n).

 

[tiny-tim]

l'Hôpital's Rule

Or you could look up "l'Hôpital's Rule" (try wikipedia or any elementary textbook on calculus).

But I agree, sutupidmath's method is the easy and obvious one in this case (and yes it is 1000)!

 

[sutupidmath]

thanks i got it, it's 1000. What is the rule called the (a^n - b^n).

i am not sure how do u call it in english, but it is merely the diference of powers i guess!