Question

http://img204.imageshack.us/img204/8272/f72fd82249d44e6b84cc138.png

Can anyone explain how you would get that answer for this limit?

Answer 1

well, the -1/216 comes from the right term ; 6^(x-1)/6(x+2) = 6^(x-1-(x+2)) = 6^-3, but I'm not sure how to get rid of the left part

Answer 2

\[{4^{x+1}-6^{x-1}\over{6^{x+2}}}={2^{2x+2}\over(2\cdot3)^{x+2}}-6^{-3}={2^x\over3^{x+2}}-6^{-3}\]since the denominator on the left will grow faster than the numerator, the first term goes to zero in the limit and we are left with \(-6^{-3}\)

Answer 3

Oooh I see thanks!

Answer 4

welcome :)