Question

求过程，谢谢🙏几道微积分求极限

Answer 1

记住在x趋于0的时候
x~sinx~tanx
而lim(x趋于无穷大) (1+1/x)^x=e
那么在这里(1) lim(x趋于0) (sinx+2tanx)/2x
=lim(x趋于0) 1/2 *sinx/x +tanx/x=1/2 +1=3/2

(2)原极限=lim(x趋于0) (2+sinx/x)/(1-2sinx/x)=(2+1)/(1-2)= -3
(3)原极限=lim(x趋于无穷大) 1/2 *sin(1/2x) /(1/2x)=1/2
(4)原极限=lim(x趋于无穷大) [(1+3/x)^(x/3)] ^3=e^3
(5)原极限=lim(x趋于无穷大) [(1-1/x)^(-x)] ^(-1/3)=e^(-1/3)
(6)原极限=lim(x趋于无穷大) { [1+4/(x-2)]^(x-2)/4 }^4x/(x-2) =e^4