1.

In the following, [x] denotes thegreatest integer less than or equal to x. {:(,"Column I",,"Column II"),(A.,x|x|,p.,"continuous in(-1, 1)"),(B.,sqrt|x|,q.,"differentiable in (-1, 1) "),(C.,x+[x],r.,"strictly increasing (-1, 1)"),(D.,|x-1|+|x+1|" in(-1,1)",s.,"not differentiable atleast at one point in(-1, 1)"):}

Answer»


Solution :A. x|x| is continuous,DIFFERENTIABLE and strictly increasing in (-1, 1).
B. `sqrt|x|` is continuous in (-1, 1) and not differentiable at x = 0.
C. x+[x] is strictly increasing in (-1, 1) and DISCONTINUOUS atx = 0
`rArr` not differentiable at x = 0.
D. `|x-1|+|x+1|=2" in "(-1, 1)`
`rArr ` The FUNCTION is continuous and differentiable in (-1, 1) .


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