If `y=sinx` and `x` changes from `pi//2` to `22//14` , what is the approximate change in `y` ?

Explanation

Take `x=pi/2`

`(x+Delta x)=22/14`
`∴dx=Δx=22/14−π/2`
Now,
`y=sinx`
`⇒(dy)/(dx)=cosx`
`=>((dy)/(dx))_(x=pi/2)=cos(pi/2)`
`=0`
`∴Δy=(dy)/(dx)Delta x`
`=0(22/14−π/2)`
`=>Δy=0`
so ,there are no change.