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The approximate value of (1.0002)^3000,...

The approximate value of `(1.0002)^3000`, is

A

`1.2`

B

`1.4`

C

`1.6`

D

`1.8`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `y=x^(3000), x=1 and x+Delta x = 1.0002`
Then, `Delta x=1.0002-1=0.0002`
Also,y=1 when x=1
Now,
`y=x^(3000)`
`rArr" "(dy)/dx=3000" "x^(2999) rArr((dy)/dx)_(x=1)=3000`
`:." "Deltay=(dy)/dxDeltax`
`rArr" "Deltay= 3000 xx0.0002 = 6/10=0.6`
Hence
`(1.0002)^(3000)= y+Deltay=1+0.6=1.6`
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