f(t)=limtx趋于无穷(x+t/x—t)的x次方

Question

f(t)=limtx趋于无穷(x+t/x—t)的x次方

Answer 1

这是1^∞型极限,用重要极限lim(x→∞) [1+(1/x)]^x=e
lim(x→∞) [(x+t)/(x-t)]^x
=lim(x→∞) [1+(2t)/(x-t)]^x
=lim(x→∞) [1+(2t)/(x-t)]^{[(x-t)/(2t)]*[(2tx)/(x-t)]}
=e^ lim(x→∞) [(2tx)/(x-t)]
=e^(2t)