Limx tends to infinity, the limit of xcos1 / x, and limx tends to the limit of 0xtanx

Limx tends to infinity, the limit of xcos1 / x, and limx tends to the limit of 0xtanx

lim(x-->∞)cos1/x=1
lim(x-->∞)x=∞
When X -- > ∞, xcos1 / X -- > ∞
lim(x-->∞)xcos1/x=∞
lim(x-->0)tanx=0
lim(x-->0)xtanx=0

Using important limit formula to find limx tends to infinity (x + A / x-a) ^ x

　　(（1+2a/x-a)^x-a/2a)^x2a/x-a=e^2a

Limx tends to the limit of 0arctan (1 / x)

1 / X - > infinity
When X - > 0 + (approaches 0 from the right) 1 / X - > positive infinity
arctan(1/x)->Pi/2
When X - > 0 - (approaches 0 from the left) 1 / X - > negative infinity
arctan(1/x)->-Pi/2
If the left and right limits are not equal, the limit does not exist