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Let psi1:[0,oo] to R , psi2:[0,oo) to R ...

Let `psi_1:[0,oo] to R , psi_2:[0,oo) to R , f:[0,oo) to R and g :[0,oo) to R` be functions such that `f(0)=g(0)=0`
`psi_1(x)=e^-x+x , x ge 0` ,
`psi_2(x)=x^2-2x-2e^-x+2 , x ge0`
`f(x)=int_(-x)^x (abs(t)-t^2)e^(-t^2)dt , x gt 0`
`g(x)=int_0^(x^2) (sqrtt)e^-t dt , x gt o`
Which of the following statements is TRUE

A

`psi_1(x) le 1` for all `x gt 1`

B

`psi_2(x) le 0` for all `x gt 1`

C

`f(x) ge 1-e^(-x^2)-2/3x^3+2/5x^5`, for all `x in (0,1/2)`

D

`g(x) le 2/3x^3-2/5x^5+1/7x^7`, for all `x in (0,1/2)`

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