For x ? R, limn→∞((x-3)/(x+2))x =
(A) e (B) e-1
(C) e-5 (D) e5

Hi Pallavi,

y=limx→∞((x-3)/(x+2))x 

=limx→∞((1-3/x)/(1+2/x))x

1^∞ form

log y = log limx→∞((x-3)/(x+2))x

y = e^{lim_x→∞xlog((1-3/x)/(1+2/x))}

y = e^{lim_x→∞[log((1-3/x)/(1+2/x))]/(1/x)}

y = e^{lim_x→∞[log((1-3/x)- log(1+2/x))]/(1/x)}

y =e^{lim_x→∞{[-3log((1-3/x)]/(-3/x)- [2log(1+2/x))](2/x)}}

y = e^-3-2 = e^-5