f(t)=lim x→无穷大 [t(1+1/x)^2tx] 求f'(t)
问题描述:
f(t)=lim x→无穷大 [t(1+1/x)^2tx] 求f'(t)
答
lim x→无穷大(1+1/x)^2tx=[lim x→无穷大(1+1/x)^x]^2t=e^(2t)
f(t)=te^(2t)
f'(t)=e^(2t)+2te^(2t)