If `y=sinxa n dx` change from `pi/2to(22)/(14),` what is the approximate change in `y ?`

Explanation

Let:


`x=frac{pi}{2} `
`
x+Delta x=frac{22}{14}`
`
Rightarrow d x=Delta x=frac{22}{14}-frac{pi}{2}=0 `

Now, ` y=sin x `
`
Rightarrow frac{d y}{d x}=cos x `
`
Rightarrow(frac{d y}{d x})_{x=frac{pi}{2}}=cos (frac{pi}{2})=0 `
`
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