Find the limit if it exist.?

Question

1) lim 1-sinx/cosx

x ->pie/2

2) Lim (x-1)/x^(2)--1

x-->1 negative

Answer 1

As x approaches pi/2, 1 approaches 1 (it may be trivial but it must be said for a complete answer) and sinx approaches 1.  It does so very slowly.

cosx approaches zero.

As x approaches pi/2, there does not exist a finite value (call it M) such that the value of sinx/cosx will always be less than M.  

Whatever gigantic number you propose for M, at some point, as x gets closer and closer to pi/2, the value of sinx/cosx will go beyond M

Therefore there is no limit (literally).