1.

Let f(x) be a non-positive continuous function and F(x)=int_(0)^(x)f(t)dt AA x ge0 and f(x) ge cF(x) where c lt 0 and let g:[0, infty) to R be a function such that (dg(x))/(dx) lt g(x) AA x gt 0 and g(0)=0 The solution set of inequation g(x)(cos^(-1)x-sin^(-1)) le0

Answer»

`[-1,1/sqrt(2)]`
`[1/sqrt(2),1]`
`[0,1/sqrt(2)]`
`[0,1/sqrt(2)]`

SOLUTION :`G(X) (COS^(-1)x-sin^(-1)x) le0`
or `(cos^(-1)x-sin^(-1)x) ge0` or `x in [-1, 1/sqrt(2)]`


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