KCET2025MathematicsContinuity and Differentiability
Match the following: In the following, [ x ] denotes the greatest integer less than or equal to x . array |l|l|l|l| & Column - I & & Column - II a . & x | x | & (i) & continuous in (-1, 1) b. & | x | & (ii) & differentiable in (-1, 1) c. & x +[ x ] & (iii) & strictly increasing in (-1, 1) d. & | x -1|+| x +1| & (iv) & not differentiable at, at least one point in (-1, 1) array
Options
- Aa-i, b-i i, c-i v, d-i i i
- Ba-i v, b-i i i, c-i, d-i i
- Ca-i i, b-i v, c-i i i, d-i
- Da - iii , b - ii , c - iv , d - i
Correct answer
C. a-i i, b-i v, c-i i i, d-i
Step-by-step solution
aligned & (a) x|x| & f(x)= array ll x^2, & x 0 -x^2 & x 0 array differentiable in (-1,1) . aligned (b) |x| = aligned x , & x 0 -x , & x 0 aligned . Not differentiable at x=0 (c) x+[x] strictly increasing in (-1,1) (d) |x-1|+|x+1|= array cc -x+1-x-1 & x -1 -x+1+x+1 & -1 x 1 x-1+x-1 & x 1 array . Continuous (-1,1)= array ccc -2 x & , & x -1 2, & -1 x 1 2 x & , & x 1 array .