Question

Find the approximate value of (4.01)⁵

Answer 1

this is the answer of this question

Answer 2

Answer:

(4.01)⁵ = 1036.8

Step-by-step explanation:

In the question,

Say,

$y=x^{5}$

On differentiating w.r.t x we get,

$\frac{dy}{dx}=5x^{4}$

Let us say x = 4.00 and Δx = 0.01,

So,

Δy = (x +  Δx)⁵ - x⁵

Δy = (4.00 + 0.01)⁵ - (4.00)⁵

Δy + 1024 = (4.01)⁵

Δy is approximately dy.

So,

$dy=(\frac{dy}{dx})\times(\Δx)$

So,

$dy=(5x^{4})\times(0.01)\\dy=(5(4.00)^{4})\times 0.01\\dy=12.8$

Therefore,

(4.01)⁵ = 1024 + 12.8 = 1036.8

(4.01)⁵ = 1036.8