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

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

Question

http://img204.imageshack.us/img204/8272/f72fd82249d44e6b84cc138.png

Can anyone explain how you would get that answer for this limit?

anonymous · Answer

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

turingtest · Answer

$${4^{x+1}-6^{x-1}\over{6^{x+2}}}={2^{2x+2}\over(2\cdot3)^{x+2}}-6^{-3}={2^x\over3^{x+2}}-6^{-3}$$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 $-6^{-3}$

anonymous · Answer

Oooh I see thanks!

turingtest · Answer

welcome :)