The value of ( 127 ) 1 / 3 to four decimal places is Options: A . &nbsp 5.0267 B . &nbsp 5.4267 C . &nbsp 5.5267 D . &nbsp 5.001

Answer: Option A : A Let y = x 1 / 3 , x = 125 and x + Δ x = 127. Then, d y d x = 1 3 x 2 / 3 a n d Δ x = 0 When, x = 125, we have y = 5 a n d d y d x = 1 75 ∴ y = d y d x Δ x ⇒ Δ y 1 75 × 2 = 2 75 ∴ ( 127 ) 1 / 3 = y + Δ y = 5 + 2 75 = 5 + 8 3 × 1 100 ⇒ ( 127 ) 1 / 3 = 5 + ( 2.6667 ) 100 = 5.02667 = 5.0267 Hence (a) is the correct answer.

The value of (127)1/3 to four decimal places is

Discussion Forum : Application Of Derivatives

Question -

The value of $(127)^{1 / 3}$ to four decimal places is

Options:

A . 5.0267

B . 5.4267

C . 5.5267

D . 5.001

Answer: Option A
:
A

Let y = $x^{1 / 3}, x = 125$ and $x + Δ x = 127.$ Then,
$\frac{d y}{d x} = \frac{1}{3 x^{2 / 3}} a n d Δ x = 0$
When, x = 125, we have
$y = 5 a n d \frac{d y}{d x} = \frac{1}{75}$
$∴ y = \frac{d y}{d x} Δ x \Rightarrow Δ y \frac{1}{75} \times 2 = \frac{2}{75}$
$∴ (127)^{1 / 3} = y + Δ y = 5 + \frac{2}{75} = 5 + \frac{8}{3} \times \frac{1}{100}$
$\Rightarrow (127)^{1 / 3} = 5 + \frac{(2.6667)}{100} = 5.02667 = 5.0267$
Hence (a) is the correct answer.

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