Question

Using differentials, find the the approximate value.

1. (29) to the power of 1/3

Answer 1

The answer is explained in the attachment.


Hope this helps!

Answer 2

Hi,

Here is your answer,

(29)¹/³

= ( 27 + 2)¹/³                                            ∴ x = 27 , δx = 2
  
Let y = x¹/³

dy = 1/3 × x⁻²/³ × dx

dy = 1/3 × (27)⁻²/³ × (2)

= 1/3 × (3³)⁻²/³ × (2)   { On cancelling 3 }

= 1/3 × 1/(3)² × (2)

= 2/(3)³ 

= 2/27

Now, by using 1st Principle 

f(x + δx/Δx) = f(x) + f'(x) × δx/Δx

             = (27)¹/³ + 2/27

             = (3³)¹/³ + 2/27      { On cancelling 3 }

              = 3 + 2/27

              = 81 + 2/27

               = 83/27

                = 3.07


Hope it helps you !