Question

lim(s->x) s^5-x^5/s^2-x^2 can someone please explain to me why this answer is not 0? i factored it out s^2-x^2 and canceled to get s^3-x^3

Answer 1

because the only common factor of the numerator and denominator is
\[s-x\]

Answer 2

\[s^5-x^5=(s-x) (s^4+s^3 x+s^2 x^2+s x^3+x^4)\]

Answer 3

ahhh wow im retard.... lol so how would you do it then?

Answer 4

so you get that in the numerator, and
\[(s-x)(s+x)\] in the denominator, can only cancel the common factor

Answer 5

got it

Answer 6

you get
\[\frac{ (s^4+s^3 x+s^2 x^2+s x^3+x^4)}{s+x}\] after canceling, then replace x by s

Answer 7

kk then factor out an x^2?

Answer 8

x*

Answer 9

nothing to factor now. your only job is
\[\lim_{s\rightarrow x}\frac{ (s^4+s^3 x+s^2 x^2+s x^3+x^4)}{s+x}\]
you no longer have a zero in the denominator, so where you see an x, replace it by s
you get a whole raft of
\[s^4\] in the numerator and
\[2s\] in the denominator. then you can cancel one of the "s"

Answer 10

oh damn i had that backwards sorry
replace the "s" by "x" etc.

Answer 11

haha yeah i figured, thank you!@