Q. 1 E3.6( 16 Votes )

# Using differentials, find the approximate value of each of the following up to 3 places of decimal.

Consider y =

Let x = 1 and Δx = -0.001. Then, we get

Δy = (x+∆x)1/10 - (x)1/10

Δy = (0.999)1/10 - 1

(0.999)1/10 = Δy + 1

Now, dy is approximately equal to Δy and is given by:

dy =

= -0.0001

Therefore, the approximate value of is 0.9999.

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