CUET Preparation Today
CUET
-- Mathematics - Section B1
Continuity and Differentiability
If [ ] denotes the greatest integer function, \underset{x→\frac{π}{2}}{\lim}\frac{5\sin[\cos x]}{[\cos x]+2} is:
0
1
∞
Does not exist
LHL = \underset{x→\frac{π^-}{2}}{\lim}\frac{5\sin[\cos x]}{[\cos x]+2}=\frac{5\sin(0)}{0+2}=0; RHL = \underset{x→\frac{π^+}{2}}{\lim}\frac{5\sin(-1)}{-1+2}=-5\sin (1)
