Question

Evaluate the limit s^5 - b^5 / s^2 - b^2 as s approaches b.

Answer 1

−b5+s5

Answer 2

−b5+s5

Answer 3

-b5+5s

Answer 4

it is easy to see s^2-b^2=(s-b)(s+b)
and the s-b on the bottom is the thing giving us problem
s-b should be a factor of s^5-b^5
you can find out by divide s^5-b^5 by s-b

Answer 5

well i tried googling a formula to simply a^5 - b^5 and i found the sum and difference of odd power. the formula i got was (a-b)(a^4 +(a^3)b + a^2b^2 -a(b^3) + b^4)

Answer 6

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

Answer 7

\[\frac{s^5-b^5}{s^2-b^2}=\frac{s^4+s^3b+s^2b^2+sb^3+b^4}{s+b}\]

Answer 8

here you haven gotten rid of the thing that will make the bottom zero

Answer 9

so now it is all about plugin' in

Answer 10

replacing s with b

Answer 11

okay i got (5b^4)/2b

Answer 12

ok sounds great

Answer 13

I think you can reduce that :)

Answer 14

also our answers works when b isn't 0

Answer 15

thanks!