Find approximate values of the following : `(1.99)^7`

Explanation

Let `y = x^7`
Then `dy = 7x^6 dx rArr deltay = 7x^6 deltax`
`rArr (x + deltax)^7 - x^7 = 7x^6 deltax`
`rArr (x + deltax)^7 = x^7 + 7x^6 cdot deltax`
Put x = 2 and `deltax = -0.01`
Then `(1.99)^7 = 2^7 - 7 xx 2^6 xx 0.01`
` = 128 - 7 xx 64 xx 0.01`
= `128 - 4.48 = 123 cdot 52`