If `P(1)=0a n d(d P(x))/(dx),sinx+2xgeq(3x(x+1))/pi` . Explain the identity, if any, used in the proof.

Explanation

We are given the `(dp(x))/(dx)ltP(x),forallxle`1 and P(1)=0
`(dPO(x))/(dx)-P(x)gt0`
Multiplying both sides by `e^(-x)` we get
`e^(x)(dp(x))/(dx)-e^(-x)p(x)gt0`
`(d)/(dx)[e^(-x)p(x)]gt0`
`e^(-x)p(x)` is and increasing function.
`forall xgt1,e^(-x)gte^(-1)P(1)=0`
`e^(-x)P(x)gt0,forallxgt1`
`P(x)gt0, forall xgt1`