1.

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

Answer»

Solution :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`


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