LIM (x approaches 0) what is cos1 / x

LIM (x approaches 0) what is cos1 / x

LIM (x approaches 0) cos1 / X
1 / X is ∞
Cos ∞ is an oscillatory function, so the limit does not exist

lim(2x-3/2x+1）^x+1

The following omitted do not write, in order to facilitate the landlord to see clearly
First of all
lim（x+1）ln（2x-3/2x+1)
=lim[ln(2x-3)-ln(2x+1)]/[1/(x+1)]
=Lim [2 / (2x-3) - 2 / (2x + 1)] / [- 1 / (x + 1) ^ 2] / / Law of lobita
=lim -8(x+1)^2/[(2x-1)(2x+3)]
=-2
therefore
Original limit
=E ^ LIM (x + 1) ln (2x-3 / 2x + 1) / / limit compound algorithm
=e^(-2)
Reminder:
For the limit function which is more complex,
It is often solved indirectly through the exponential logarithmic transformation and the limit rule of composite function